Feed forward exhaust throttle and wastegate control for an engine

ABSTRACT

Controlling an exhaust gas temperature of an engine. An electronic control unit receives a parameter setpoint command, monitors parameters of an engine using a plurality of sensors, receives measured engine states based on the monitored engine parameters from the plurality of sensors, generates measured engine state estimates and controlled engine state estimates using an engine observer model, determines an observer error based on a difference between the measured engine states and the measured engine state estimates, generates model corrections based on the observer error, generates a desired exhaust throttle valve position using an inverse engine model based on the parameter setpoint command, the controlled engine state estimates, and the model corrections, and adjusts a position of the exhaust throttle valve based on the desired exhaust throttle position.

BACKGROUND

This disclosure relates to controlling an engine.

SUMMARY

Diesel engines sometimes use exhaust throttles to regulate exhausttemperature by modifying the fuel-to-air (“F/A”) ratio as well as enginepumping work. For example, an exhaust throttle is used to control thetemperature of exhaust gasses going to an engine after-treatment system.Exhaust throttle control can incorporate various protections to preventhigh intake manifold pressure, high cylinder pressure, high exhaustmanifold pressure, and high turbine speed. Previously, exhaust throttleand exhaust gas temperature control was achieved using a combination ofopen loop setpoint tables and proportional-integral-derivative (“PID”)controllers. Operational constraints were controlled by separate PIDcontrollers and subsequent arbitration of valve position commands. Dueto the dynamics of such systems, PID based control is relatively slowand unresponsive to dynamic or transient operating conditions.

This disclosure replaces the open loop setpoint tables and PID controlswith a physics-based feed forward system that provides improved responseunder transient conditions, prioritizes control objectives, accounts forsystem constraints, and is easier to calibrate than existing systems.The disclosure employs an air system state observer for an engine toestimate parameters that are not and/or cannot be measured directly.Sensor information is also used to make corrections to an engineobserver model. The models and corrections from the air system stateobserver are used in feed forward calculations to determine the desiredexhaust throttle position, a desired wastegate valve position, and adesired exhaust gas recirculation (“EGR”) valve position that achievedesired performance objectives. Feed forward control with this methodprovides fast and accurate control of the engine within the constraintsof the system. The air system state observer is a model of the engineair system that runs in a controller or engine control unit (“ECU”) insubstantially real time and receives the same actuator commands as thereal engine. Differences between measured engine states and estimatedengine states are used with an observer controller to make correctionsto the engine observer model. Information from the engine observer modeland model corrections from the observer controller are used in feedforward calculations to determine the desired exhaust throttle valveposition, wastegate valve position, and EGR valve position. The airsystem state observer eliminates the need for various prior controlloops and provides more robust engine control. The feed forwardcalculations include engine cylinder models, EGR cooler and valvemodels, EGR mixer models, compressor and charge air cooler (“CAC”)models, turbine and wastegate models, and exhaust throttle models. As aresult, this disclosure improves engine control under transientconditions, improves operation in corner conditions (i.e., extremeoperational conditions), limits control to stay within constraints, andis easier to calibrate.

In one embodiment, this disclosure provides a method of controllingexhaust gas temperature for an engine. The engine includes an air systemhaving an exhaust throttle valve. The method includes receiving aparameter setpoint command at an inverse engine model, monitoringparameters of the engine using a plurality of sensors, receivingmeasured engine states based on the monitored engine parameters from theplurality of sensors, and generating measured engine state estimates andcontrolled engine state estimates using an engine observer model. Thecontrolled engine state estimates are received by the inverse enginemodel. The method also includes determining an observer error based on adifference between the measured engine states and the measured enginestate estimates and generating model corrections based on the observererror. The model corrections are received by the inverse engine model.The method also includes generating a desired exhaust throttle valveposition using the inverse engine model based on the parameter setpointcommand, the controlled engine state estimates, and the modelcorrections, and adjusting a position of the exhaust throttle valvebased on the desired exhaust throttle position.

In another embodiment, this disclosure provides a system for controllingexhaust gas temperature. The system includes an engine, a plurality ofsensors, and an electronic control unit. The engine includes an airsystem and an exhaust throttle valve. The plurality of sensors are usedto monitor parameters of the engine. The electronic control unitincludes a processor and a memory. The electronic control unit isoperable to receive a parameter setpoint command at an inverse enginemodel, monitor parameters of the engine using the plurality of sensors,receive measured engine states based on the monitored engine parametersfrom the plurality of sensors, and generate measured engine stateestimates and controlled engine state estimates using an engine observermodel. The controlled engine state estimates are received by the inverseengine model. The electronic control unit is also operable to determinean observer error based on a difference between the measured enginestates and the measured engine state estimates and generate modelcorrections based on the observer error. The model corrections arereceived by the inverse engine model. The electronic control unit isalso operable to generate a desired exhaust throttle valve positionusing the inverse engine model based on the parameter setpoint command,the controlled engine state estimates, and the model corrections, andadjust a position of the exhaust throttle valve based on the desiredexhaust throttle position.

Before any embodiments are explained in detail, it is to be understoodthat the disclosure is not limited in its application to the details ofthe configuration and arrangement of components set forth in thefollowing description or illustrated in the accompanying drawings. Thisdisclosure is capable of other embodiments and of being practiced or ofbeing carried out in various ways. Also, it is to be understood that thephraseology and terminology used herein are for the purpose ofdescription and should not be regarded as limiting. The use of“including,” “comprising,” or “having” and variations thereof herein aremeant to encompass the items listed thereafter and equivalents thereofas well as additional items. Unless specified or limited otherwise, theterms “mounted,” “connected,” “supported,” and “coupled” and variationsthereof are used broadly and encompass both direct and indirectmountings, connections, supports, and couplings.

In addition, it should be understood that embodiments of the disclosuremay include hardware, software, and electronic components or modulesthat, for purposes of discussion, may be illustrated and described as ifthe majority of the components were implemented solely in hardware.However, one of ordinary skill in the art, and based on a reading ofthis detailed description, would recognize that, in at least oneembodiment, the electronic based aspects of the disclosure may beimplemented in software (e.g., stored on non-transitorycomputer-readable medium) executable by one or more processing units,such as a microprocessor and/or application specific integrated circuits(“ASICs”). As such, it should be noted that a plurality of hardware andsoftware based devices, as well as a plurality of different structuralcomponents may be utilized. For example, “servers” and “computingdevices” described in the specification can include one or moreprocessing units, one or more computer-readable medium modules, one ormore input/output interfaces, and various connections (e.g., a systembus) connecting the components.

Other aspects of the disclosure will become apparent by consideration ofthe detailed description and accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a vehicle including an engine.

FIG. 2 illustrates a control system for the vehicle of FIG. 1.

FIG. 3 illustrates an engine control system that includes proportionalintegral derivative (“PID”) controllers and output control arbitration.

FIG. 4 illustrates an engine control system that includes an air systemstate observer and control system.

FIG. 5 illustrates a generalized state observer.

FIG. 6 is an engine air system schematic diagram.

FIG. 7 illustrates an air system state observer and control system.

FIG. 8 illustrates an inverse engine model and control system.

FIG. 9 is an iterative searching process for determining turbine outletpressure.

FIG. 10 is an iterative searching process for determining wastegateposition.

FIG. 11 is an iterative searching process for determining turbineinterstage pressure.

FIG. 12 a wastegate actuator and solenoid control system.

DETAILED DESCRIPTION

This disclosure provides a feed forward control system for controllingthe operation of an engine (e.g., a diesel engine) by controlling anexhaust gas recirculation (“EGR”) valve, an exhaust throttle valve, anda wastegate valve. The control system includes an electronic controlunit (“ECU”) that is used to implement the feed forward control system.The ECU includes an air system state observer for the engine that isused to estimate parameters that are not and/or cannot be measureddirectly. Models used by, and corrections generated by, the air systemstate observer are used in feed forward calculations to determine adesired exhaust throttle position, a desired wastegate valve position,and a desired EGR valve position that achieve desired performanceobjectives. Feed forward control with this method provides fast andaccurate control of the engine within the constraints of the system. Thefeed forward calculations include engine cylinder models, EGR cooler andvalve models, EGR mixer models, compressor and charge air cooler (“CAC”)models, turbine and wastegate models, and exhaust throttle models. Themodels are used, for example, to calculate minimum and maximum turbineflow to provide exhaust manifold pressure control within a given rangeand to calculate an exhaust throttle valve position that provides adesired turbine delta pressure without exceeding flow limits requiredfor exhaust manifold pressure protection. The disclosures providedherein can be implemented in, or applied to, a variety of applicationsthat include an engine and an exhaust throttle.

FIG. 1 illustrates a vehicle 100 that includes a diesel engine. Althoughthe vehicle 100 illustrated in FIG. 1 is a tractor, the control systemsand techniques described herein can be implemented in other vehicles,such as lawn mowers, utility vehicles, dump trucks, loaders, dozers,skid steers, excavators, bunchers, harvesters, etc. For descriptivepurposes, the disclosure is described herein generally with respect to avehicle that includes a diesel engine. This disclosure can, however, beapplied to any apparatus or machine that includes a diesel engine andthe association of the disclosure with a vehicle is only exemplary.

FIG. 2 illustrates an electronic control unit (“ECU”) or controller 200associated with the vehicle 100 or another vehicle or apparatus thatincludes a diesel engine. The ECU 200 illustrated in FIG. 2 is, forexample, an ECU for a diesel engine. The ECU 200 is connected or coupledto a variety of additional modules or components, such as a userinterface module 205, one or more indicators 210, a power supply module215, a plurality of sensors 220, an exhaust throttle control module 225,a wastegate control module 230, an exhaust gas recirculation (“EGR”)control module 235, a data store or database 240, and an engine controlmodule 245, and engine 250. The exhaust throttle control module 225, thewastegate control module 230, the EGR control module 235, and the enginecontrol module 245 are shown as being separate from and connected to theECU 200 for illustrative purposes. Each of these modules canalternatively be implemented entirely within the ECU 200 such that theECU is configured, operable, or programmed to be an engine control unitfor the engine 250. As is described herein, the modules 225, 230, 235,and 245 are connected to or associated with one another to achieve thedesired control of the engine 250. The plurality of sensors 220 are, forexample, temperature sensors, pressure sensors, position sensors (e.g.,valve position sensors), humidity sensors, etc.

The ECU 200 includes combinations of hardware and software that areprogrammed, configured, and/or operable to, among other things, controlthe operation of the vehicle 100 and or engine 250, control activationof (e.g., current through) a wastegate solenoid, control a wastegatevalve position, control an EGR valve position, control an exhaustthrottle valve position, activate the one or more indicators 210 (e.g.,a liquid crystal display [“LCD”], one or more LEDs, etc.), monitor theoperation of the vehicle 100 and/or engine 250, etc. In someembodiments, the ECU 200 includes a plurality of electrical andelectronic components that provide power, operational control, andprotection to the components and modules within the ECU 200, the vehicle100, and/or the engine 250. For example, the ECU 200 includes, amongother things, a processing unit 255 (e.g., a microprocessor, amicrocontroller, or another suitable programmable device), a memory 260,input units 265, and output units 270. The processing unit 255 includes,among other things, a control unit 275, an arithmetic logic unit (“ALU”)280, and a plurality of registers 285 (shown as a group of registers inFIG. 2), and can be implemented using a known computer architecture,such as a modified Harvard architecture, a von Neumann architecture,etc. The processing unit 255, the memory 260, the input units 265, andthe output units 270, as well as the various modules connected to theECU 200 are connected by one or more control and/or data buses (e.g.,common bus 290). The control and/or data buses are shown generally inFIG. 2 for illustrative purposes. The use of one or more control and/ordata buses for the interconnection between and communication among thevarious modules and components would be known to a person skilled in theart in view of this disclosure. In some embodiments, the ECU 200 isimplemented partially or entirely on a semiconductor chip, is afield-programmable gate array (“FPGA”), is an application specificintegrated circuit (“ASIC”), etc.

The memory 260 includes, for example, a program storage area and a datastorage area. The program storage area and the data storage area caninclude combinations of different types of memory, such as read-onlymemory (“ROM”), random access memory (“RAM”) (e.g., dynamic RAM[“DRAM”], synchronous DRAM [“SDRAM”], etc.), electrically erasableprogrammable read-only memory (“EEPROM”), flash memory, a hard disk, anSD card, or other suitable magnetic, optical, physical, or electronicmemory devices or data structures. The processing unit 255 is connectedto the memory 260 and executes software instructions that are capable ofbeing stored in a RAM of the memory 260 (e.g., during execution), a ROMof the memory 260 (e.g., on a generally permanent basis), or anothernon-transitory computer readable medium such as another memory or adisc. Software and instructions included in the implementation of thevehicle 100 and/or engine 250 can be stored in the memory 260 of the ECU200. The software includes, for example, firmware, one or moreapplications, program data, filters, rules, one or more program modules,and other executable instructions. The ECU 200 is configured, operable,or programmed to retrieve from the memory 260 and execute, among otherthings, instructions related to the control processes and methodsdescribed herein. In other constructions, the ECU 200 includesadditional, fewer, or different components or modules.

The user interface module 205 is used to control or monitor the vehicle100 and/or engine 250 (e.g., is within a cabin of the vehicle 100). Theuser interface module 205 can include a combination of digital andanalog input or output devices required to achieve a desired level ofcontrol and monitoring for the vehicle 100. For example, the userinterface module 205 can include a display and input devices such as atouch-screen display, one or more knobs, dials, switches, buttons, etc.The display is, for example, a liquid crystal display (“LCD”), alight-emitting diode (“LED”) display, an organic LED (“OLED”) display,an electroluminescent display (“ELD”), a surface-conductionelectron-emitter display (“SED”), a field emission display (“FED”), athin-film transistor (“TFT”) LCD, etc. In other constructions, thedisplay is a Super active-matrix OLED (“AMOLED”) display. The userinterface module 205 can also be configured to display conditions ordata associated with the vehicle 100 and/or engine 250 in real-time orsubstantially real-time. For example, the user interface module 205 isconfigured to display sensed or measured temperatures, pressures, valvepositions, diluent-to-air (“D/A”) ratios, fuel-to-air (“F/A”) ratios,etc. In some embodiments, the user interface module 205 is controlled inconjunction with the one or more indicators 210 (e.g., LEDs) to providevisual indications of the status or conditions of the vehicle 100 and/orengine 250.

FIG. 3 illustrates an existing engine control system 300 that utilizesproportional-integral-derivative (“PID”) control with output controlarbitration. The system 300 is not described in detail herein. However,the system 300 includes PID control modules 305 and 310, as well asoutput control arbitration modules 315, 320, and 325. The system 300 isimplemented with feedback control to determine a desired EGR valveposition, a variable-geometry turbocharger (“VGT”) position, and an airthrottle position. The PID control modules 305 and 310 calculate thedesired positions, and the output controls 315, 320, and 325 prevent thesystem 300 from operating an engine outside of its operational limits.As a result of the feedback controls, PID control modules 305 and 310,and the output control arbitration modules 315, 320, and 325, the system300 is relatively slow and unresponsive to dynamic or transientoperating conditions.

FIG. 4 illustrates an engine control system 400 including an air systemstate observer and control module or unit 405. The system 400 providesquicker and more efficient control of the engine 250 than the system 300of FIG. 3. The system 400 includes a setpoint tables module 410, a firstfactors and offsets module 415, a second factors and offsets module 420,a first limits module 425, a second limits module 430, a smoke factormodule 435, a setpoint offsets module 440, an after-treatment systemmodule (e.g., a diesel oxidation catalyst [“DOC”] inlet temperaturecontrol module) 445, the air system state observer and control system405, an EGR valve position control module 450, a wastegate positioncontrol module 455, and an exhaust throttle position control module 460.The setpoint tables module 410 receives a variety of inputs 465 relatedto, for example, engine speed, desired amount of fuel (e.g., percylinder of the engine 250), torque-speed curve information, and controlmode settings. The setpoint tables modules 410 outputs a variety offactors, such as an EGR valve maximum position, a DOC inlet temperaturesetpoint, a D/A ratio setpoint, and an F/A ratio setpoint. The factorsand offsets modules 415 and 420 can also receive a variety of inputs 470and 475, respectively, such as ambient temperature multipliers, ambientpressure multipliers, etc. The smoke factor module 435 can receiveinputs 480 such as a smoke opacity F/A ratio limit, an F/A ratioestimate, etc. The modules of system 400 described so far are similar tomodules shown in the system 300 of FIG. 3 and will not be described indetail herein.

The DOC inlet temperature control module 445, the air system stateobserver and control system 405, the EGR valve position control module450, the wastegate position control module 455, and the exhaust throttleposition control module 460, however, differ from the system 300 of FIG.3. In FIG. 4, the air system state observer and control system 405receives a desired diluent-to-air ratio, D/A_(des), a desiredfuel-to-air ratio, F/A_(des), and a desired exhaust manifold deltapressure for a temperature change, ΔP_(em) _(_) _(des). The air systemstate observer and control system 405 also receives a variety ofadditional sensed temperatures, pressures, speeds, etc., as describedbelow. The air system state observer and control system 405 outputs adesired EGR valve position, u_(egr) _(_) _(des), a desired wastegateposition, u_(wg) _(_) _(des), and a desired exhaust throttle position,u_(et) _(_) _(des), for controlling an EGR valve, a wastegate solenoid,and an exhaust throttle using the EGR valve position control module 450,the wastegate position control module 455, and the exhaust throttleposition control module 460, respectively. The EGR valve positioncontrol module 450 outputs an EGR valve control signal 485 (e.g., acontrol signal having a duty cycle corresponding to the desired EGRvalve position). The wastegate position control module 455 outputs awastegate solenoid control signal 490 (e.g., a control signal having aduty cycle corresponding to the desired wastegate position). The exhaustthrottle position control module 460 outputs an exhaust throttleposition control signal 495 (e.g., a control signal having a duty cyclecorresponding to the desired exhaust throttle position). The operationthe air system state observer and control system 405 is described indetail below.

FIG. 5 illustrates a generalized state observer control system 500 thatincludes a state observer 505. The state observer 505 is a mathematicalmodel of a process that is being controlled and executed by the ECU 200.The state observer control system 500 that includes a physical process510 that is being modeled by a process model 515, as well as an observercontroller 520, a feedback controller 525 and a feed forward controller530. The feed forward controller 530 is an inverse of the process model515. The process model 515 is not a perfect model of the physicalprocess 510 because the physical process 510 experiences disturbances535 that are not accounted for by the process model 515. Sensors used tomonitor the physical process 510 provide a measured state 540, and theprocess model 515 outputs a measured state estimate 545. The differencebetween the measured state 540 and the measured state estimate 545provides an observer error 550 that is input to the observer controller520. The observer controller 520 processes the observer error 550 andgenerates a model correction 555 that is input to the process model 515and to the feed forward controller 530. Setpoint commands 560 indicatingdesired values for process parameters are input to the control system500. The setpoint commands 560 are input to the feed forward controller530. The difference between the setpoint commands 560 and a controlledstate estimate 565 generated by the process model 515 produces a controlerror 570 that is input to the feedback controller 525. The sum of theoutputs of the feedback controller 525 and the feed forward controller530 produces actuator commands 575 that are input to the physicalprocess 510 and the process model 515.

There are a variety of advantages to implementing a state observerwithin an engine control system. The state observer can provideestimates of states that are difficult, expensive, and/or impossible tomeasure directly (e.g., fewer sensors may be required). The processmodel 515 with corrections from the observer controller 520 can be usedin the feed forward calculation of the actuator commands 575. Theinverse process model 530 has desired states or setpoint commands 560 asinputs, and the corresponding actuator commands 575 are the outputs.Feed forward control of this type provides fast response and can reducethe complexity of feedback control. Such a technique can also make iteasier to implement system constraints because the constraints can betreated as limits within the feed forward and feedback control, thuseliminating the need for separate controllers for modifying the actuatorcommands (i.e., output arbitration control). Using an observer 505 inthe control system 500 can also improve the operation of an engine innon-standard conditions because the model 515 can predict the effects ofchanges and adjust the controls as needed.

The generalized state observer control system 500 of FIG. 5 is adaptedfor use in an engine 250 (e.g., a diesel engine) to control the airsystem of the engine 250. A schematic view of an engine and air system600 is illustrated in FIG. 6. The engine system 600 illustrates variouscomponents, state variables, mass flows, and sensors used to control anEGR valve 605, an exhaust throttle valve 610, and a wastegate valve 615.Air enters the system 600 at a compressor inlet into a low pressurecompressor 620. A temperature sensor 625, a pressure sensor 630, and ahumidity sensor 635 are located at the inlet to the low pressurecompressor 620. The low pressure compressor 620 compresses the air andsends it to a high pressure compressor 640 where it is furthercompressed. The compressed air from the high pressure compressor 640 isinput to a charge air cooler (“CAC”) 645. Various parameters, forexample, pressure, temperature and diluent mass fraction in the CAC 645can be monitored. The output from the CAC 645 passes to a mixer 650. Atemperature sensor 655 and a pressure sensor 660 are positioned betweenthe CAC 645 and the mixer 650 to measure the CAC outlet temperature andpressure.

The mixer 650 mixes fresh air from the CAC 645 and recirculated exhaustgasses from an exhaust gas recirculation (“EGR”) cooler 665. Atemperature sensor 670 and a pressure sensor 675 are positioned betweenthe EGR cooler 665 and the EGR valve 605 to measure the temperature andpressure at the outlet of the EGR cooler 665. The mixed gasses from themixer 650 are fed to an engine intake manifold 680, and the output ofthe engine intake manifold 680 is divided among a plurality of cylinders685 of the engine 250. The engine 250 of FIG. 6 is illustrated asincluding six cylinders. In some embodiments, the engine 250 includes adifference number of cylinders (e.g., two cylinders, four cylinders, 8cylinders, etc.). A temperature sensor 695 and a pressure sensor 700 arepositioned with respect to the intake manifold 680 to measure thetemperature and pressure of the intake manifold 680.

The exhaust gasses from the cylinders 685 of the engine 250 are fed toan engine exhaust manifold 705. The exhaust gasses from the exhaustmanifold 705 are either recirculated through the EGR cooler 665 orexpelled from the system 600. A temperature sensor 710 and a pressuresensor 715 are positioned with respect to the exhaust manifold 705 tomeasure the temperature and pressure of the exhaust manifold 705. Someof the exhaust gasses expelled from the exhaust manifold 705 passthrough a high pressure turbine 720 and a low pressure turbine 725 of aturbocharger. The high pressure turbine 720 can be controlled using thewastegate valve 615. The low pressure turbine 725 can be controlledusing the exhaust throttle valve 610.

Additionally, a position sensor 730 is used to measure the position ofthe EGR valve 605 and generate a corresponding output signal. A positionsensor 735 is used to measure the position of the exhaust throttle 610and generate a corresponding output signal. In some embodiments, aposition sensor 740 is used to measure the position of the wastegatevalve 615 and generate a corresponding output signal. In someembodiments, a position sensor 745 is used to measure the position of awastegate solenoid 750 that is used to control the wastegate valve 615.In some embodiments, additional parameters such as additional pressures,additional temperatures, engine speeds, turbocharger speeds, exhaustback pressure, etc., are also measured and/or monitored within thesystem 600 by additional sensors 220 and the ECU 200.

The system 600 shown in FIG. 6 can be modeled by the ECU 200 using stateequations that are based on the conservation of mass, energy, andmomentum. Some relationships can be approximated using, for example,first order filters. Each state equation describes a rate of change. Thestate value at any given time can then be determined by integrating thestate equation. Within the ECU 200, each state of the engine 250 and/orsystem 600 can be given an initial condition, and a state value at eachtime step of the ECU 200 can be updated using numeric integration. Thestate equations for the system 600 are described below with continuedreference to the system 600 of FIG. 6. Values for various parametersdescribed herein are calculated or determined estimations or estimatedvalues for the parameter unless the parameter or value for the parameteris referred to as a sensed value or sensed parameter, or the parameteror value for the parameter is described as being received from aphysical sensor (e.g., a temperature sensor, a pressure sensor, etc.).

A rate of change of mass in the CAC 645,

$\frac{{dm}_{cac}}{dt},$

is modeled by the difference between the mass flow coming in from thecompressors 620, 640, {dot over (m)}_(cmp), and the mass flow exitingthe CAC 645, {dot over (m)}_(caco), as shown below in EQN. 1:

$\begin{matrix}{\frac{{dm}_{cac}}{dt} = {{\overset{.}{m}}_{cmp} - {\overset{.}{m}}_{caco}}} & {{EQN}.\mspace{14mu} 1}\end{matrix}$

A rate of change of mass in the intake manifold 680,

$\frac{{dm}_{im}}{dt},$

is modeled by the sum of the mass flows exiting the CAC 645, {dot over(m)}_(caco), and the EGR valve 605, {dot over (m)}_(egr), minus the massflow entering the engine 250, {dot over (m)}_(cylsi), as shown below inEQN. 2:

$\begin{matrix}{\frac{{dm}_{im}}{dt} = {{\overset{.}{m}}_{caco} + {\overset{.}{m}}_{egr} - {\overset{.}{m}}_{cylsi}}} & {{EQN}.\mspace{14mu} 2}\end{matrix}$

The rate of change of diluent mass in the intake manifold 680,

$\frac{{dm}_{d\_ im}}{dt},$

is modeled as the sum of the mass flow exiting the CAC 645, {dot over(m)}_(caco), multiplied by the mass fraction of diluent in the CAC 645,χ_(d) _(_) _(cac), (we can assume it is the same as the mass fraction ofwater in ambient air due to humidity) plus the mass flow entering fromthe EGR valve 605, {dot over (m)}_(egr), multiplied by the mass fractionof diluent in the exhaust manifold 705, χ_(d) _(_) _(em), minus the massflow entering the cylinders 685 of the engine 250, {dot over(m)}_(cylsi), multiplied by the mass fraction of diluent in the intakemanifold 680, χ_(d) _(_) _(im), as shown below in EQN. 3:

$\begin{matrix}{\frac{{dm}_{d\_ im}}{dt} = {{{\overset{.}{m}}_{caco} \cdot \chi_{d\_ cac}} + {{\overset{.}{m}}_{egr} \cdot \chi_{d\_ em}} - {{\overset{.}{m}}_{cylsi} \cdot \chi_{d\_ im}}}} & {{EQN}.\mspace{14mu} 3}\end{matrix}$

The term diluent is used herein to describe everything other than dryair or fuel that is included in a mixture.

A rate of change of mass in the exhaust manifold 705,

$\frac{{dm}_{em}}{dt},$

is modeled by the mass flow exiting the cylinders 685 of the engine 250,{dot over (m)}_(cylso), minus the mass flow entering the EGR cooler 665,{dot over (m)}_(egr), and the mass flow entering the high pressure andlow pressure turbines 720, 725, {dot over (m)}_(trb), as shown below inEQN. 4:

$\begin{matrix}{\frac{{dm}_{em}}{dt} = {{\overset{.}{m}}_{cylso} - {\overset{.}{m}}_{egr} - {\overset{.}{m}}_{trb}}} & {{EQN}.\mspace{14mu} 4}\end{matrix}$

A rate of change of diluent mass in the exhaust manifold 705,

$\frac{{dm}_{d\_ em}}{dt},$

is modeled by the difference between the mass flow exiting the cylinders685 of the engine 250, {dot over (m)}_(cylso), multiplied by the massfraction of diluent exiting the cylinders 685 of the engine 250, χ_(d)_(_) _(cylso), and the sum of the mass flows entering the EGR cooler665, {dot over (m)}_(egr), and the high and low pressure turbines 720,725, {dot over (m)}_(lp) _(_) _(trb), multiplied by the mass fraction ofdiluent in the exhaust manifold 705, χ_(d) _(_) _(em), as shown below inEQN. 5:

$\begin{matrix}{\frac{m_{d\_ em}}{t} = {{{\overset{.}{m}}_{cylso} \cdot \chi_{d\_ cylso}} - {\left( {{\overset{.}{m}}_{egr} + {\overset{.}{m}}_{lp\_ trb}} \right) \cdot \chi_{d\_ em}}}} & {{EQN}.\mspace{14mu} 5}\end{matrix}$

A rate of change of temperature at the output of the CAC 645,

$\frac{T_{caco}}{t},$

is modeled by the difference between the steady state temperature at theoutput of the CAC 645, T_(caco) _(_) _(ss), and the measured temperatureat the output of the CAC 645, T_(caco), divided by a time constant forthe CAC 645, τ_(cac), as shown below in EQN. 6:

$\begin{matrix}{\frac{T_{caco}}{t} = \frac{\left( {T_{caco\_ ss} - T_{caco}} \right)}{\tau_{cac}}} & {{EQN}.\mspace{14mu} 6}\end{matrix}$

A rate of change of temperature at the output of the EGR cooler 665,

$\frac{T_{egrco}}{t},$

is modeled by the difference between the steady state temperature at theoutput of the EGR cooler 665, T_(egrco) _(_) _(ss), and the measuredtemperature at the output of the EGR cooler 665, T_(egrco), divided by atime constant for the EGR cooler 665, τ_(egrc), as shown below in EQN.7:

$\begin{matrix}{\frac{T_{egrco}}{t} = \frac{\left( {T_{{egr}{co\_ ss}} - T_{egrco}} \right)}{\tau_{egrc}}} & {{EQN}.\mspace{14mu} 7}\end{matrix}$

The steady state cooler outlet temperatures T_(caco) _(_) _(ss) andT_(egrco) _(_) _(ss) can be calculated using a heat exchangereffectiveness model. The effectiveness can be calibrated using a tablewith mass flow as the input. An effectiveness of “1” means the cooleroutlet temperature is equal to the temperature of the cooling fluid, andan effectiveness of “0” means there is no change in temperature betweenthe cooler inlet and outlet.

A rate of temperature change of the intake manifold 680,

$\frac{T_{im}}{t},$

is calculated using the mass flows in and out, the temperature in andout, and the change in mass within the intake manifold 680. The rate ofchange of temperature of the intake manifold

$\frac{T_{im}}{t}$

is modeled by the rate of change of mass at the output of the CAC 645,{dot over (m)}_(caco), multiplied by the specific heat at constantpressure, C_(P), multiplied by the temperature at the output of the CAC645, T_(caco), plus the mass flow of the EGR valve 605, {dot over(m)}_(egr), multiplied by specific heat at constant pressure, C_(P),multiplied by the temperature at the output of the EGR cooler 665,T_(egrco) minus the mass flow entering the cylinders 685 of the engine250, {dot over (m)}_(cylsi), multiplied by specific heat at constantpressure, C_(P), multiplied by the temperature of the intake manifold,T_(im), minus the rate of change of mass in the intake manifold 680,

$\frac{m_{im}}{t},$

multiplied by specific heat at constant volume, C_(V), multiplied by thetemperature of the intake manifold 680, T_(im), all divided by theproduct of the mass in the intake manifold 680, m_(im), multiplied bythe specific heat at constant volume, C_(V), as shown below in EQN. 8:

$\begin{matrix}{\frac{T_{im}}{t} = \frac{\begin{matrix}{{{\overset{.}{m}}_{caco} \cdot C_{p} \cdot T_{caco}} + {{\overset{.}{m}}_{egr} \cdot C_{p} \cdot T_{egrco}} -} \\{{{\overset{.}{m}}_{cylsi} \cdot C_{p} \cdot T_{im}} - {\frac{m_{im}}{t} \cdot V_{v} \cdot T_{im}}}\end{matrix}}{m_{im} \cdot C_{v}}} & {{EQN}.\mspace{14mu} 8}\end{matrix}$

The specific heats can be measured experimentally at constant volume orconstant pressure. The specific heat at constant pressure, C_(P), isgreater than the specific heat at constant volume, C_(V), because as amixture is heated at constant pressure it expands and does work on thecontainer or the fluid around it. The specific heat at constantpressure, C_(P), can be used to calculate energy flow into or out of acontrol volume. The specific heat at constant volume, C_(V), can be usedto calculate the change in energy within the control volume due tochanges in temperature and mass.

A rate of change of temperature at the exhaust manifold 705,

$\frac{T_{em}}{t},$

is modeled by the difference between the temperature at the output ofthe cylinders 685 of the engine 250, T_(cylso), and the temperature ofthe exhaust manifold 705, T_(em), divided by a time constant, τ_(em),for the exhaust manifold 705, as shown below in EQN. 9:

$\begin{matrix}{\frac{T_{em}}{t} = \frac{\left( {T_{cylso} - T_{em}} \right)}{\tau_{em}}} & {{EQN}.\mspace{14mu} 9}\end{matrix}$

A rate of change of the speed of the low pressure turbocharger 725,

$\frac{N_{lpt}}{t},$

is modeled by the sum of the torques on the low pressure turbine shaftand blades divided by the inertia of the low pressure turbocharger shaftand blades (i.e., Newton's second law for rotation). The sum of thetorques is modeled by the difference between low pressure turbine power,{dot over (W)}_(lp) _(_) _(trb), and low pressure compressor power, {dotover (W)}_(lp) _(_) _(cmp), divided by the low pressure turbochargerspeed, N_(lpt). The turbine power or compressor power can be calculatedfrom the change in enthalpy of the gas as it goes through the turbine orcompressor. The enthalpy change is equal to the mass flow ratemultiplied by the specific heat at constant pressure, C_(p), multipliedby the delta temperature across the turbine or compressor. When turbinespeed is expressed in units of revolutions per minute (“RPM”), turbinespeed can be converted to radians per second (“rad/s”) using a factor ofπ/30. The inverse of this factor is squared in EQN. 10 to convert thelow pressure turbocharger speed, N_(lpt), in the denominator and also toexpress the solution,

$\frac{N_{lpt}}{t},$

in units of revolutions per minute per second (rpm/s).

$\begin{matrix}{\frac{N_{lpt}}{t} = {\frac{1}{J_{lpt}} \cdot \left( \frac{{\overset{.}{W}}_{lp\_ trb} - {\overset{.}{W}}_{lp\_ cmp}}{N_{lpt}} \right) \cdot \left( \frac{30\text{/}\pi \mspace{14mu} {rpm}}{{rad}\text{/}s} \right)^{2}}} & {{EQN}.\mspace{14mu} 10}\end{matrix}$

A rate of change in the speed of the high pressure turbocharger,

$\frac{N_{hpt}}{t},$

is modeled by the sum of the torques on the high pressure turbine shaftand blades divided by the inertia of the high pressure turbochargershaft and blades (i.e., Newton's second law for rotation). The sum ofthe torques is modeled by the difference between high pressure turbinepower, {dot over (W)}_(hp) _(_) _(trb), and high pressure compressorpower, {dot over (W)}_(hp) _(_) _(cmp), divided by the high pressureturbocharger speed, N_(hpt). The turbine power or compressor power canbe calculated from the change in enthalpy of the gas as it goes throughthe turbine or compressor. The enthalpy change is equal to the mass flowrate multiplied by the specific heat at constant pressure, C_(p),multiplied by the delta temperature across the turbine or compressor.When turbine speed is expressed in units of RPM, turbine speed can beconverted to rad/s using a factor of π/30. The inverse of this factor issquared in EQN. 11 to convert high pressure turbocharger speed, N_(hpt),in the denominator and also to express the solution,

$\frac{N_{hpt}}{t},$

in units of revolutions per minute per second (rpm/s).

$\begin{matrix}{\frac{N_{hpt}}{t} = {\frac{1}{J_{hpt}} \cdot \left( \frac{{\overset{.}{W}}_{h\; p\; \_ \; {trb}} - {\overset{.}{W}}_{h\; p\; \_ \; {cmp}}}{N_{hpt}} \right) \cdot \left( \frac{{30/\pi}\mspace{14mu} {rpm}}{{rad}\text{/}s} \right)^{2}}} & {{EQN}.\mspace{14mu} 11}\end{matrix}$

In addition to the state equations (i.e., EQNS. 1-11) associated withthe engine system 600, cylinder masses associated with the materials inthe cylinders 685 (i.e., entering the cylinders 685 and exiting thecylinders 685) are also used to control the engine system 600. Thecylinders 685 of the engine 250 are described with respect to the massof material entering a cylinder. The total mass of material entering acylinder 685, m_(cyli), is calculated based on the pressure in theintake manifold 680, P_(im), the volume of the cylinder 685, V_(cyl)_(_) _(disp), the volumetric efficiency, VE, of the cylinder 685 (e.g.,based on engine speed to fuel tables), the temperature of the intakemanifold 680, T_(im), and the ideal gas constant, R, as shown below inEQN. 12:

$\begin{matrix}{m_{cyli} = \frac{P_{i\; m} \cdot V_{{cyl}\; \_ \; {disp}} \cdot {VE}}{R \cdot T_{i\; m}}} & {{EQN}.\mspace{14mu} 12}\end{matrix}$

The material entering the cylinder 685 is part diluent and part air. Thediluent mass entering the cylinder 685, m_(d) _(_) _(cyli), iscalculated by multiplying the mass of material entering the cylinder685, m_(cyli), by the mass fraction of diluent in the intake manifold680, χ_(d) _(_) _(im), as shown below in EQN. 13:

m _(d) _(_) _(cyli) =m _(cyli)·χ_(d) _(_) _(im)  EQN. 13

An air mass entering the cylinder 685, m_(a) _(_) _(cyli), is calculatedby multiplying the mass of material entering the cylinder 685, m_(cyli),by the difference between one and the mass fraction of diluent in theintake manifold 680, χ_(d) _(_) _(im), as shown below in EQN. 14:

m _(a) _(_) _(cyli) =m _(cyli)·(1−χ_(d) _(_) _(im))  EQN. 14

An amount of residual mass remaining in the cylinder 685, m_(res),(e.g., gasses remaining from one cycle of the cylinder to the next cycleof the cylinder) is calculated based on the pressure in the exhaustmanifold 705, P_(em), the clearance volume between the piston and thecylinder head when the piston is at top-dead-center (“TDC”), V_(cyl)_(_) _(clear), a residual mass correction factor, CF_(res), for thecylinder 685, the temperature of the output of the cylinder 685,T_(cyclo), and the ideal gas constant, R, as shown below in EQN. 15:

$\begin{matrix}{m_{res} = \frac{P_{em} \cdot V_{{cyl}\; \_ \; {clear}} \cdot {CF}_{res}}{R \cdot T_{cylo}}} & {{EQN}.\mspace{14mu} 15}\end{matrix}$

Residual material remaining in the cylinder 685 is also part diluent andpart air. The diluent mass remaining in the cylinder 685, m_(d) _(_)_(res), is calculated by multiplying the mass of residual materialremaining in the cylinder 685, m_(res), by the mass fraction of diluentat the output of the cylinder 685, χ_(d) _(_) _(cylso), as shown belowin EQN. 16:

m _(d) _(_) _(res) =m _(res)·χ_(d) _(_) _(cylso)  EQN. 16

An air mass remaining in the cylinder 685, m_(a) _(_) _(res), iscalculated by multiplying the mass of residual material remaining in thecylinder 685, m_(res), by the difference between one and the massfraction of diluent at the output of the cylinder 685, χ_(d) _(_)_(cylso), as shown below in EQN. 17:

m _(a) _(_) _(res) =m _(res)·(1−χ_(d) _(_) _(cylso))  EQN. 17

A mass of material in the cylinder 685 (i.e., when the intake valvecloses), m_(cyl), can then be calculated as the sum total mass ofmaterial entering the cylinder 685, m_(cyli), and the mass of residualmaterial remaining in the cylinder 685 from a previous cycle, m_(res)_(_) _(previous), as shown below in EQN. 18:

m _(cyl) =m _(cyli) +m _(res) _(_) _(previous)  EQN. 18

A total mass of material in the cylinder 685, m_(cyl), is also comprisedof diluent and air, and each portion can be calculated. The mass ofdiluent in the cylinder 685, m_(d) _(_) _(cyl), can be calculated as thesum of the mass of diluent entering the cylinder 685, m_(d) _(_)_(cyli), and the mass of residual diluent from the previous cycle, m_(d)_(_) _(res) _(_) _(previous), as shown below in EQN. 19:

m _(d) _(_) _(cyl) =m _(d) _(cyli) +m _(d) _(_) _(res) _(_)_(previous)  EQN. 19

Similarly, a mass of air in the cylinder 685, m_(a) _(_) _(cyl), can becalculated as the sum of the mass of air entering the cylinder 685,m_(a) _(_) _(cyli), and the mass of residual air from the previouscycle, m_(a) _(_) _(res) _(_) _(previous), as shown below in EQN. 20:

m _(a) _(_) _(cyl) =m _(a) _(_) _(cyli) +m _(a) _(_) _(res) _(_)_(previous)  EQN. 20

A mass of material exiting the cylinder 685, m_(cylo), can be calculatedas the mass of material entering the cylinder 685, m_(cyli), plus themass of fuel in the cylinder 685, m_(f), plus the mass of residualmaterial remaining in the cylinder 685 from a previous cycle, m_(res)_(_) _(previous), minus the mass of residual material remaining in thecylinder 685, m_(res), as shown below in EQN. 21:

m _(cylo)=^(m) _(cyli) +m _(f) +m _(res) _(_) _(previous) −m_(res)  EQN. 21

A mass flow entering the cylinder 685, {dot over (m)}_(cylsi), and themass flow exiting the cylinder 685 can then be calculated based on themass of material entering the cylinder, m_(cyli), and the mass ofmaterial exiting the cylinder, m_(cylo), respectively. The mass flowentering the cylinder 685 is calculated based on the speed of the engine250, N_(e), the number of cylinders in the engine 250, n_(cyls), and themass of material entering the cylinder 685, m_(cyli), as shown below inEQN. 22:

$\begin{matrix}{{\overset{.}{m}}_{cylsi} = \frac{N_{e} \cdot n_{cyls} \cdot m_{cyli}}{\left( {2\mspace{14mu} {rev}\text{/}{cycle}} \right) \cdot \left( {60\mspace{14mu} \sec \text{/}\min} \right)}} & {{EQN}.\mspace{14mu} 22}\end{matrix}$

The mass flow entering the cylinder 685, {dot over (m)}_(cylsi) isconverted for an intake event occurring every two revolutions of theengine 250 by dividing by two revolutions per cycle multiplied by 60seconds per minute.

Similarly, the mass flow exiting the cylinder, {dot over (m)}_(cylso),is calculated based on the speed of the engine 250, N_(e), the number ofcylinders in the engine 250, n_(cyls), and the mass of material exitingthe cylinder 685, m_(cylo), as shown below in EQN. 23:

$\begin{matrix}{{\overset{.}{m}}_{cylso} = \frac{N_{e} \cdot n_{cyls} \cdot m_{cylo}}{\left( {2\mspace{14mu} {rev}\text{/}{cycle}} \right) \cdot \left( {60\mspace{14mu} \sec \text{/}\min} \right)}} & {{EQN}.\mspace{14mu} 23}\end{matrix}$

Again, the mass flow exiting the cylinder 685, {dot over (m)}_(cylso),is converted for an intake event occurring every two revolutions of theengine 250 by dividing by two revolutions per cycle multiplied by 60seconds per minute.

The inlet and outlet temperatures of each cooler 645 and 665 can bemodeled and/or the temperatures can be measured. Half of the cooler canbe assumed to be at the inlet temperature and half of the cooler can beassumed to be at the outlet temperature. The average cooler density canbe calculated using the average temperature and average pressure.Assuming a linear drop in pressure and temperate across the cooler, theaverage temperature and average pressure can be calculated by averaginginlet and outlet values. The mass flow out for each cooler 645 and 665can be calculated by multiplying the average density by the table outputand then taking the square root. A CAC mass flow correction factorCF_(cac) and an EGR mass flow correction factor CF_(egr) can be includedin these mass flow calculations for the coolers 645 and 665, as shownbelow in EQNS. 24 and 25:

$\begin{matrix}{{\overset{.}{m}}_{caco} = {{CF}_{cac} \cdot \sqrt{\rho_{{cac}\; \_ \; {avg}} \cdot {{CACFlowSqOverDensityTbl}\left( {{\Delta \; P_{cac}},{\Delta \; T_{cac}}} \right)}}}} & {{EQN}.\mspace{14mu} 24} \\{{\overset{.}{m}}_{egrco} = {{CF}_{egrc} \cdot \sqrt{\rho_{{egrc}\; \_ \; {avg}} \cdot {{EGRCFlowSqOverDensityTbl}\left( {{\Delta \; P_{egrc}},{\Delta \; T_{egrc}}} \right)}}}} & {{EQN}.\mspace{14mu} 25}\end{matrix}$

The CAC mass flow correction factor, CF_(cac), can be applied as acorrection to the compressor mass flow estimates and the CAC mass flowestimates. The EGR mass flow correction factor, CF_(egr), can be appliedas a correction to the EGR cooler mass flow estimates and the EGR valvemass flow estimates.

The mass flows for the EGR valve 605, the wastegate valve 615, and theexhaust throttle 610 can be modeled using the compressible gas flowequation for an orifice, as shown below in EQNS. 26, 27, and 28,respectively:

$\begin{matrix}{{\overset{.}{m}}_{egrv} = {{CF}_{egrv} \cdot {C_{d\; \_ \; {egr}}\left( u_{egr} \right)} \cdot A_{egr} \cdot \frac{P_{egrco}}{\sqrt{R \cdot T_{egrco}}} \cdot {\Psi \left( \frac{P_{i\; m}}{P_{egrco}} \right)}}} & {{EQN}.\mspace{14mu} 26} \\{\mspace{20mu} {{\overset{.}{m}}_{wg} = {{CF}_{trb} \cdot {C_{d\; \_ \; {wg}}\left( u_{wg} \right)} \cdot A_{wg} \cdot \frac{P_{em}}{\sqrt{R \cdot T_{em}}} \cdot {\Psi \left( \frac{P_{{trb}\; \_ \; {inter}}}{P_{em}} \right)}}}} & {{EQN}.\mspace{14mu} 27} \\{\mspace{20mu} {{\overset{.}{m}}_{et} = {{CF}_{trb} \cdot {C_{d\; \_ \; {et}}\left( u_{et} \right)} \cdot A_{et} \cdot \frac{P_{trbo}}{\sqrt{R \cdot T_{trbo}}} \cdot {\Psi \left( \frac{P_{doci}}{P_{trbo}} \right)}}}} & {{EQN}.\mspace{14mu} 28}\end{matrix}$

where C_(d) _(_) _(egr) is the discharge coefficient for the EGR valve605, which can be calibrated using a table with EGR valve position,u_(egr), as the input, C_(d) _(_) _(wg) is the discharge coefficient forthe wastegate 615, which can be calibrated using a table with wastegatevalve position, u_(wg), as the input and C_(d) _(_) _(et) is thedischarge coefficient for the exhaust throttle 610, which can becalibrated using a table with exhaust throttle position, u_(et), as theinput. The areas, A, can be calculated using actuator bore diameters.The term, R, is the ideal gas constant. The compressible gas flowfunction, Ψ, is a function of pressure ratio and can be calibrated usinga table with pressure ratio as the input. The table values can becalculated off-line using EQNS. 29 and 30:

$\begin{matrix}{{{\Psi \left( \frac{P_{out}}{P_{i\; n}} \right)} = {\left( \frac{P_{out}}{P_{i\; n}} \right)^{\frac{1}{k}} \cdot \sqrt{\frac{2 \cdot k}{k + 1} \cdot \left( {1 - \left( \frac{P_{out}}{P_{i\; n}} \right)^{\frac{k - 1}{k}}} \right)}}}{{{for}\mspace{14mu} \left( \frac{P_{out}}{P_{i\; n}} \right)} \geq \left( \frac{2}{k + 1} \right)^{\frac{k}{k - 1}}}} & {{EQN}.\mspace{14mu} 29} \\{{{\Psi \left( \frac{P_{out}}{P_{i\; n}} \right)} = \sqrt{k \cdot \left( \frac{2}{k + 1} \right)^{\frac{k + 1}{{k - 1}\;}}}}{{{for}\mspace{14mu} \left( \frac{P_{out}}{P_{i\; n}} \right)} < \left( \frac{2}{k + 1} \right)^{\frac{k}{k - 1}}}} & {{EQN}.\mspace{14mu} 30}\end{matrix}$

where the term, k, represents the ratio of specific heats C_(p)/C_(v).

The state equations, cylinder masses, and engine mass flows describedabove can then be used to control the engine 250 using the air systemstate observer and control system 405. FIG. 7 illustrates the air systemstate observer and control system 405 from FIG. 4 in more detail. In thesystem 405, desired in-cylinder states are converted to manifold states.The desired mass flows to achieve the manifold states are calculated,and flow models and model corrections are used to calculate the desiredactuator positions for the engine 250. The control system 405 includesthe engine 250, an engine observer model 800, an observer controller805, and an inverse engine model 810.

The engine 250 experiences disturbances 815 (e.g., deposits in engine,air leaks, valves not opening, etc.) that are not modeled by the engineobserver model 815. Sensors monitoring the engine 250 provide a measuredstate 820. The engine observer model 800 processes various inputs(including, for example, speeds, masses, pressures, temperatures, modelcorrections, etc.) and generates a measured state estimate 825 to becompared with the measured state 820, as well as controlled stateestimates 830 that are provided to the inverse engine model 810. Theengine observer model includes, for example, state equations, mass flowequations, and cylinder equations corresponding to EQNS. 1-30 above. Thedifference between the measured state 820 and the measured stateestimate 825 provides an observer error 835 that is input to theobserver controller 805. The observer controller 805 generates modelcorrections 840 that are provided to the engine observer model 800 andthe inverse engine model 810. The model corrections generated by theobserver controller 805 can include an integral term that drives thesteady state error to zero. This can help keep the operation of theengine observer model 800 close to that of the engine 250.

The inverse engine model or feed forward controller 810 takes thecontrolled state estimates 830 generated by the engine observer model800, the model corrections 840 generated by the observer controller 805,the desired state inputs 845, and various other system parameters andcalculates desired engine state commands 850 to achieve the desireddiluent-to-air ratio, D/A_(des), and fuel-to-air ratio, F/A_(des),values included in the desired state inputs 845.

The inverse engine module 810 of FIG. 7 is illustrated in more detail inFIG. 8. The inverse engine module 810 includes a cylinders model module900, a feed forward and closed loop EGR control module 905, an EGRcooler and Valve model module 910, an EGR mixer model module 915, acompressor and CAC model module 920, an EGR cooler and valve modelmodule 925, a limits and filter module 930 and exhaust pressure controlmodule 935, a turbine and wastegate model module 940, an exhaustthrottle model module 945, and a wastegate solenoid control module 950.

The inverse engine module 810 is divided into two primary controlportions: an EGR control portion 955; and an exhaust throttle andwastegate control portion 960 (i.e., a turbocharger control portion).The cylinders model module 900 receives the desired diluent-to-airratio, D/A_(des), and the desired fuel-to-air ration, F/A_(des). Thecylinders model 900 outputs a desired intake manifold diluent massfraction for fast control χ_(d) _(_) _(im) _(_) _(fast) _(_) _(des), tothe feed forward and closed loop EGR control module 905. The desiredintake manifold diluent mass fraction for fast control χ_(d) _(_) _(im)_(_) _(fast) _(_) _(des), is calculated by the cylinders model module900 and using EQNS. 31-33. A desired cylinder diluent mass for fastcontrol, m_(d) _(_) _(cyl) _(_) _(fast) _(_) _(des) (i.e., EGR valvecontrol), is equal to the desired diluent-to-air ratio, D/A_(des),multiplied by a cylinder air mass, m_(a) _(_) _(cyl), as shown below inEQN. 31:

m _(d) _(_) _(cyl) _(_) _(fast) _(_) _(des) =D/A _(des) ·m _(a) _(_)_(cyl)  EQN. 31

A desired cylinder-in diluent mass for fast control, m_(d) _(_) _(cyli)_(_) _(fast) _(_) _(des), is equal to the desired cylinder diluent massfor fast control, m_(d) _(_) _(cyl) _(_) _(fast) _(_) _(des), minus acylinder residual diluent mass, m_(d) _(_) _(res), as shown below inEQN. 32:

m _(d) _(_) _(cyli) _(_) _(fast) _(_) _(des) =m _(d) _(_) _(cyl) _(_)_(fast) _(_) _(des) −m _(d) _(_) _(res)  EQN. 32

The desired intake manifold diluent mass fraction for fast control,χm_(d) _(_) _(im) _(_) _(fast) _(_) _(des), is then equal to the desiredcylinder in diluent mass for fast control, m_(d) _(_) _(cyli) _(_)_(fast) _(_) _(des), divided by a cylinder in mass estimate, m_(cycli),as shown below in EQN. 33:

$\begin{matrix}{\chi_{d\; \_ \; {im}\; \_ \; {fast}\; \_ \; {des}} = \frac{m_{d\; \_ \; {cyli}\; \_ \; {fast}\; \_ \; {des}}}{m_{cyli}}} & {{EQN}.\mspace{14mu} 33}\end{matrix}$

The feed forward and closed loop EGR control module 905 receives thedesired intake manifold diluent mass fraction for fast control χ_(d)_(_) _(im) _(_) _(fast) _(_) _(des), a mass flow into the enginecylinders, {dot over (m)}_(cylsi), a CAC diluent mass fraction, χ_(d)_(_) _(cac), an exhaust manifold diluent mass fraction, χ_(d) _(_)_(em), and an intake manifold diluent mass fraction, χ_(d) _(_) _(im).

A desired intake manifold EGR mass fraction for fast control, χ_(egr)_(_) _(im) _(_) _(fast) _(_) _(des) (i.e., EGR valve control), iscalculated by taking the difference between the desired intake manifolddiluent mass fraction for fast control χ_(d) _(_) _(im) _(_) _(fast)_(_) _(des), and a CAC diluent mass fraction estimate, χ_(d) _(_)_(cac), and then dividing by a difference between the exhaust manifolddiluent mass fraction, χ_(d) _(_) _(em), and the CAC diluent massfraction, χ_(d) _(_) _(cac), as shown below in EQN. 34. The CAC diluentmass fraction, χ_(d) _(_) _(cac), will be non-zero when there ishumidity in the ambient air. The CAC diluent mass fraction is calculatedusing a humidity measurement from the humidity sensor 635 at the lowpressure compressor inlet.

$\begin{matrix}{\chi_{{egr}\; \_ \; i\; m\; \_ \; {fast}\; \_ \; {des}} = \frac{\chi_{d\; \_ \; {im}\; \_ \; {fast}\; \_ \; {des}} - \chi_{d\; \_ \; {cac}}}{\chi_{d\; \_ \; {em}} - \chi_{d\; \_ \; {cac}}}} & {{EQN}.\mspace{14mu} 34}\end{matrix}$

A feed forward EGR mass flow, {dot over (m)}_(egr) _(_) _(ff), iscalculated by multiplying the mass flow into cylinders, {dot over(m)}_(cylsi), by the desired intake manifold EGR mass fraction for fastcontrol, χ_(egr) _(_) _(im) _(_) _(fast) _(_) _(des), as shown below inEQN. 35:

{dot over (m)} _(egr) _(_) _(ff) ={dot over (m)} _(cylsi)·χ_(egr) _(_)_(im) _(_) _(fast) _(_) _(des)  EQN.35

A closed loop EGR mass flow, {dot over (m)}_(egr) _(_) _(cl), iscalculated by multiplying an EGR mass flow proportional gain, K_(p) _(_)_(egr), by the difference between the desired intake manifold diluentmass fraction for fast control χ_(d) _(_) _(im) _(_) _(fast) _(_)_(des), and the intake manifold diluent mass fraction, χ_(d) _(_) _(im),as shown below in EQN. 36:

{dot over (m)} _(egr) _(_) _(cl) =K _(p) _(_) _(egr)·(χ_(d) _(_) _(im)_(_) _(fast) _(_) _(des)−χ_(d) _(_) _(im))  EQN.36

A desired EGR mass flow for fast control, {dot over (m)}_(egr) _(_)_(fast) _(_) _(des), is equal to the sum of the feed forward EGR massflow, {dot over (m)}_(egr) _(_) _(ff), and closed loop EGR mass flow,{dot over (m)}_(egr) _(_) _(cl), as shown below in EQN. 37:

{dot over (m)} _(egr) _(_) _(fast) _(_) _(des) ={dot over (m)} _(egr)_(_) _(ff) +{dot over (m)} _(egr) _(_) _(cl)  EQN. 37

The desired EGR mass flow for fast control, {dot over (m)}_(egr) _(_)_(fast) _(_) _(des), is output to the EGR cooler and valve model module910. The EGR cooler and valve model module 910 also receives an exhaustmanifold pressure, P_(em), an intake manifold pressure, P_(im), anexhaust manifold temperature, T_(em), the EGR cooler mass flowcorrection factor, CF_(egrc), the EGR valve mass flow correction factor,CF_(egrv), and an EGR cooler outlet temperature, T_(egrco).

A desired EGR valve position, U_(egr) _(_) _(des), is then determinedusing EQNS. 25 and 26. EQN. 25 is used to find a desired EGR cooleroutlet pressure that provides flow equal to the desired EGR mass flowfor fast control, {dot over (m)}_(egr) _(_) _(fast) _(_) _(des) (e.g.,using an iterative solving process). EQN. 26 is then used to find thedesired EGR valve position, U_(egr) _(_) _(des), that provides flowequal to the desired EGR mass flow for fast control, {dot over(m)}_(egr) _(_) _(fast) _(_) _(des), with desired EGR cooler outletpressure, P_(egrco) _(_) _(des).

The cylinders model 900 also outputs a desired cylinder in mass, {dotover (m)}_(cylsi) _(_) _(des), a desired intake manifold diluent massfraction for slow control, χ_(d) _(_) _(im) _(_) _(slow) _(_) _(des),and a desired exhaust manifold diluent mass fraction, χ_(d) _(_) _(em)_(_) _(des), to the EGR mixer module 915.

A desired cylinder air mass, m_(a) _(_) _(cyl) _(_) _(des), is equal toa fuel mass injected into a cylinder, m_(f), divided by a desired fuelto air ratio, F/A_(des), as shown below in EQN. 38:

$\begin{matrix}{m_{a\; \_ \; {cyl}\; \_ \; {des}} = \frac{m_{f}}{F/A_{des}}} & {{EQN}.\mspace{14mu} 38}\end{matrix}$

A cylinder in air mass estimate, m_(a) _(_) _(cyl) _(_) _(des), is equalto the desired cylinder air mass, m_(a) _(_) _(cyl) _(_) _(des), minusthe previous cylinder residual air mass estimate, m_(a) _(_) _(res) _(_)_(previous), as shown below in EQN. 39:

m _(a) _(_) _(cyli) _(_) _(des) =m _(a) _(_) _(cyl) _(_) _(des) −m _(a)_(_) _(res) _(_) _(previous)  EQN. 39

A desired cylinder diluent mass for slow control, m_(d) _(_) _(cyl) _(_)_(slow) _(_) _(des) (i.e., wastegate and exhaust throttle control), isequal to the desired diluent-to-air ratio, D/A_(des), multiplied by thedesired cylinder air mass, m_(a) _(_) _(cyl) _(_) _(des), as shown belowin EQN. 40.

m _(d) _(_) _(cyl) _(_) _(slow) _(_) _(des) =D/A _(des) ·m _(a) _(_)_(cyl) _(_) _(des)  EQN. 40

A desired cylinder in diluent mass for slow control, m_(d) _(_) _(cyli)_(_) _(slow) _(_) _(des), is equal to the desired cylinder diluent massfor slow control, m_(d) _(_) _(cyl) _(_) _(slow) _(_) _(des), minus theprevious cylinder residual diluent mass estimate, m_(d) _(_) _(res) _(_)_(previous), as shown below in EQN. 41:

m _(d) _(_) _(cyli) _(_) _(slow) _(_) _(des) =m _(d) _(_) _(cyl) _(_)_(slow) _(_) _(des) −m _(d) _(_) _(res) _(_) _(previous)  EQN. 41

A desired cylinder in mass, m_(cyli) _(_) _(des), is equal to thedesired cylinder in air mass, m_(a) _(_) _(cyli) _(_) _(des), plus thedesired cylinder in diluent mass for slow control, m_(d) _(_) _(cyl)_(_) _(slow) _(_) _(des), as shown below in EQN. 42:

m _(cyli) _(_) _(des) =m _(a) _(_) _(cyli) _(_) _(des) +m _(d) _(_)_(cyli) _(_) _(slow) _(_) _(des)  EQN. 42

The desired mass flow into the cylinders, {dot over (m)}_(cylsi) _(_)_(des), is then calculated using engine speed, N_(e), the number ofengine cylinders, n_(cyls), and the desired cylinder in mass, m_(cyli)_(_) _(des), as shown below in EQN. 43:

$\begin{matrix}{{\overset{.}{m}}_{{cylsi}\; \_ \; {des}} = \frac{N_{e} \cdot n_{cyls} \cdot m_{{cyli}\; \_ \; {des}}}{\left( {2\mspace{14mu} {rev}\text{/}{cycle}} \right) \cdot \left( {60\mspace{14mu} \min \text{/}\sec} \right)}} & {{EQN}.\mspace{14mu} 43}\end{matrix}$

The desired intake manifold pressure, P_(im) _(_) _(des), is equal tothe desired cylinder in mass, m_(cyli) _(_) _(des), multiplied by theideal gas constant, R, multiplied by an intake manifold temperature,T_(im), divided by a cylinder displacement volume, V_(cyl) _(_) _(disp),and volumetric efficiency, VE, as shown below in EQN. 44:

$\begin{matrix}{P_{i\; m\; \_ \; {des}} = \frac{m_{{cyli}\; \_ \; {des}} \cdot R \cdot T_{i\; m}}{V_{{cyl}\; \_ \; {disp}} \cdot {VE}}} & {{EQN}.\mspace{14mu} 44}\end{matrix}$

The desired intake manifold diluent mass fraction for slow control,χ_(d) _(_) _(im) _(_) _(slow) _(_) _(des), is equal to the desiredcylinder in diluent mass for slow control, m_(d) _(_) _(cyli) _(_)_(slow) _(_) _(des), divided by cylinder in mass estimate, m_(cyli) _(_)_(des), as shown below in EQN. 45:

$\begin{matrix}{\chi_{d\; \_ \; i\; m\; \_ \; {slow}\; \_ \; {des}} = \frac{m_{d\; \_ \; {cyli}\; \_ \; {slow}\; \_ \; {des}}}{m_{{cyli}\; \_ \; {des}}}} & {{EQN}.\mspace{11mu} 45}\end{matrix}$

The desired exhaust manifold diluent mass fraction χ_(d) _(_) _(em) _(_)_(des), is determined using EQNS. 46-48. A desired cylinder mass whenthe exhaust valve opens, m_(cyl) _(_) _(evo) _(_) _(des), is equal tothe desired cylinder air mass, m_(a) _(_) _(cyl) _(_) _(des), plus thedesired cylinder diluent mass for slow control, m_(d) _(_) _(cyl) _(_)_(slow) _(_) _(des), plus a fuel mass injected into the cylinder, m_(f),as shown below in EQN. 46:

m _(cyl) _(_) _(evo) _(_) _(des) =m _(a) _(_) _(cyl) _(_) _(des) +m _(d)_(_) _(cyl) _(_) _(slow) _(_) _(des) +m _(f)  EQN. 46

A desired cylinder diluent mass when the exhaust valve opens, m_(d) _(_)_(cyl) _(_) _(evo) _(_) _(des), is equal to the desired cylinder diluentmass for slow control, m_(d) _(_) _(cyl) _(_) _(slow) _(_) _(des), plusfuel mass injected into the cylinder, m_(f), multiplied by the quantityone plus one over the Stoichiometric fuel-to-air ratio, F/A_(stoich), asshown below in EQN. 47:

$\begin{matrix}{m_{{d\_ cyl}{\_ evo}{\_ des}} = {m_{{d\_ cyl}{\_ slow}{\_ des}} + {m_{f}\left( {1 + \frac{1}{F/A_{stoich}}} \right)}}} & {{EQN}.\mspace{11mu} 47}\end{matrix}$

The desired exhaust manifold diluent mass fraction, χ_(d) _(_) _(em)_(_) _(des), is then equal to the desired cylinder diluent mass when theexhaust valve opens, m_(d) _(_) _(cyli) _(_) _(evo) _(_) _(des), dividedby the desired cylinder mass when the exhaust valve opens, m_(cyl) _(_)_(evo) _(_) _(des), as shown below in EQN. 48:

$\begin{matrix}{\chi_{{d\_ em}{\_ des}} = \frac{m_{{d\_ cyl}{\_ evo}{\_ des}}}{m_{{cyl\_ evo}{\_ des}}}} & {{EQN}.\mspace{11mu} 48}\end{matrix}$

The EGR mixer module 915 receives the desired cylinder in mass flow,{dot over (m)}_(cylsi) _(_) _(des), the desired intake manifold diluentmass fraction for slow control, χ_(d) _(_) _(im) _(_) _(slow) _(_)_(des), and the desired exhaust manifold diluent mass fraction, χ_(d)_(_) _(em) _(_) _(des). The EGR mixer module 915 generates a desiredcompressor mass flow, {dot over (m)}_(cmp) _(_) _(des), and a desiredEGR mass flow for slow control, {dot over (m)}_(egr) _(_) _(slow) _(_)_(des).

A desired intake manifold EGR mass fraction for slow control, χ_(egr)_(_) _(im) _(_) _(slow) _(_) _(des) (i.e., for wastegate and exhaustthrottle control), is calculated by taking the difference between thedesired intake manifold diluent mass fraction for slow control, χ_(d)_(_) _(im) _(_) _(slow) _(_) _(des), and the CAC diluent mass fraction,χ_(d) _(_) _(cac), and then dividing by the difference between thedesired exhaust manifold diluent mass fraction, χ_(d) _(_) _(em) _(_)_(des), and the CAC diluent mass fraction, χ_(d) _(_) _(cac), as shownbelow in EQN. 49:

$\begin{matrix}{\chi_{{egr\_ im}{\_ slow}{\_ des}} = \frac{\chi_{{d\_ im}{\_ slow}{\_ des}} - \chi_{d\_ cac}}{\chi_{{d\_ em}{\_ des}} - \chi_{d\_ cac}}} & {{EQN}.\mspace{11mu} 49}\end{matrix}$

The desired EGR mass flow for slow control, {dot over (m)}_(egr) _(_)_(slow) _(_) _(des), is then equal to the desired mass flow intocylinders, {dot over (m)}_(cylsi) _(_) _(des), multiplied by the desiredintake manifold EGR mass fraction for slow control, χ_(egr) _(_) _(im)_(_) _(slow) _(_) _(des), as shown below in EQN. 50:

{dot over (m)} _(egr) _(_) _(slow) _(_) _(des) ={dot over (m)} _(cylsi)_(_) _(des)·χ_(egr) _(_) _(im) _(_) _(slow) _(_) _(des)  EQN. 50

The desired compressor mass flow, {dot over (m)}_(cmp) _(_) _(des), isequal to the difference between the desired mass flow into cylinders,{dot over (m)}_(cylsi) _(_) _(des), and the desired EGR mass flow forslow control, {dot over (m)}_(egr) _(_) _(slow) _(_) _(des), as shownbelow in EQN. 51:

{dot over (m)} _(cmp) _(_) _(des) ={dot over (m)} _(cylsi) _(_) _(des)−{dot over (m)} _(egr) _(_) _(slow) _(_) _(des)  EQN. 51

The compressor and CAC model module 920 receives the desired compressormass flow, {dot over (m)}_(cmp) _(_) _(des), as well as the desiredintake manifold pressure, P_(im) _(_) _(des). The compressor and CACmodels are used to determine how much power, {dot over (W)}_(trb) _(_)_(des), is required to achieve the desired compressor mass flow, {dotover (m)}_(cmp) _(_) _(des), with the desired intake manifold pressure,P_(im) _(_) _(des). To determine the pressure drop across the CAC 645, acompressor outlet pressure, P_(cmpo), and intake manifold pressure,P_(im), are measured or calculated from mass and temperature stateestimates using the ideal gas law.

The compressor outlet pressure, P_(cmpo), is equal to the CAC mass,m_(cac), multiplied by the ideal gas constant, R, multiplied by theaverage temperature of the CAC (i.e., the sum of compressor outlettemperature, T_(cmpo), and CAC outlet temperature, T_(caco), divided bytwo), all divided by the CAC volume, V_(cac), as shown below in EQN. 52:

$\begin{matrix}{P_{cmpo} = {\frac{m_{cac} \cdot R}{V_{cac}} \cdot \left( \frac{T_{cmpo} + T_{caco}}{2} \right)}} & {{EQN}.\mspace{11mu} 52}\end{matrix}$

The intake manifold pressure, P_(im), is equal to the intake manifoldmass, m_(im), multiplied by the ideal gas constant, R, multiplied by theintake manifold temperature, T_(im), divided by the intake manifoldvolume, V_(im), as shown below in EQN. 53:

$\begin{matrix}{P_{im} = \frac{m_{im} \cdot R \cdot T_{im}}{V_{im}}} & {{EQN}.\mspace{11mu} 53}\end{matrix}$

A desired compressor outlet pressure, P_(cmpo) _(_) _(des), is equal tothe desired intake manifold pressure, P_(im) _(_) _(des), plus thecompressor outlet pressure, P_(cmpo), minus the intake manifoldpressure, P_(im), as shown below in EQN. 54:

P _(cmpo) _(_) _(des) =P _(im) _(_) _(des)+(P _(cmpo) −P _(im))  EQN. 54

The compressor outlet pressure, P_(cmpo), and intake manifold pressure,P_(im), were previously calculated for the air system state observer andcontrol system 405, so they can conveniently be used in EQN. 54. Someerror can be introduced when calculating desired compressor outletpressure, P_(cmpo) _(_) _(des), in this way under transient conditionsbecause the pressure drop across the CAC 645 is for a present flowinstead of a desired flow. In some embodiments, EQN. 24 is used to solvefor the CAC pressure drop at the desired compressor mass flow, {dot over(m)}_(cmp) _(_) _(des). EQN. 24 would produce a more accuratecalculation, but would involve an iterative solution.

A desired compressor interstage pressure, P_(cmp) _(_) _(inter) _(_)_(des), is determined using a current compressor interstage pressure,P_(cmp) _(_) _(inter), and current compressor outlet pressure, P_(cmpo).An interpolation factor is calculated using the current pressures, andthe desired compressor interstage pressure, P_(cmp) _(_) _(inter) _(_)_(des), is calculated to be the same fractional distance between thecompressor inlet pressure, P_(cmpi), and the desired compressor outletpressure, P_(cmpo) _(_) _(des), as shown below in EQN. 55:

$\begin{matrix}{P_{{cmp\_ inter}{\_ des}} = {P_{cmpi} + {\left( \frac{P_{cmp\_ inter} - P_{cmpi}}{P_{cmpo} - P_{cmpi}} \right) \cdot \left( {P_{cmpo\_ des} - P_{cmpi}} \right)}}} & {{EQN}.\mspace{11mu} 55}\end{matrix}$

A desired high pressure compressor pressure ratio, r_(p) _(_) _(hp) _(_)_(cmp) _(_) _(des), is equal to the desired compressor outlet pressure,P_(cmpo) _(_) _(des), divided by the desired compressor interstagepressure, P_(cmp) _(_) _(inter) _(_) _(des), as shown below in EQN. 56:

$\begin{matrix}{r_{{p\_ hp}{\_ cmp}{\_ des}} = \frac{P_{cmpo\_ des}}{P_{{cmp\_ inter}{\_ des}}}} & {{EQN}.\mspace{11mu} 56}\end{matrix}$

A desired low pressure compressor pressure ratio, r_(p) _(_) _(lp) _(_)_(cmp) _(_) _(des), is equal to the desired compressor interstagepressure, P_(cmp) _(_) _(inter) _(_) _(des), divided by the compressorinlet pressure, P_(cmpi), as shown below in EQN. 57:

$\begin{matrix}{r_{{p\_ lp}{\_ cmp}{\_ des}} = \frac{P_{{cmp\_ inter}{\_ des}}}{P_{cmpi}}} & {{EQN}.\mspace{11mu} 57}\end{matrix}$

A desired high pressure compressor delta temperature, ΔT_(hp) _(_)_(cmp) _(_) _(des), is calculated using the ratio of specific heats, k,and a high pressure compressor efficiency, ε_(hp) _(_) _(cmp), as shownbelow in EQN. 58. The efficiency, ε_(hp) _(_) _(cmp), is determined inthe air system state observer and control system 405 using a compressorefficiency map. The map is a table lookup with corrected turbo speed onone axis and pressure ratio of the other axis. The efficiency isdetermined using the current pressure ratio instead of the desiredpressure ratio.

$\begin{matrix}{{\Delta \; T_{{hp\_ cmp}{\_ des}}} = \frac{r_{{p\_ hp}{\_ cmp}{\_ des}^{{({k - 1})}/k}} - 1}{ɛ_{hp\_ cmp}}} & {{EQN}.\mspace{11mu} 58}\end{matrix}$

A desired low pressure compressor delta temperature, ΔT_(lp) _(_) _(cmp)_(_) _(des), is calculated using the ratio of specific heats and a lowpressure compressor efficiency, ε_(lp) _(_) _(cmp), as shown below inEQN. 59:

$\begin{matrix}{{\Delta \; T_{{l{p\_ cmp}}{\_ des}}} = \frac{r_{{{p\_ l}p}{\_ cmp}{\_ des}^{{({k - 1})}/k}} - 1}{ɛ_{l{p\_ cmp}}}} & {{EQN}.\mspace{11mu} 59}\end{matrix}$

A desired compressor power, {dot over (W)}_(cmp) _(_) _(des), is equalto the desired compressor mass flow, {dot over (m)}_(cmp) _(_) _(des),multiplied by the specific heat at constant pressure, C_(p), multipliedby the desired low pressure compressor delta temperature, ΔT_(lp) _(_)_(cmp), plus the desired high pressure compressor delta temperature,ΔT_(hp) _(_) _(cmp), as shown below in EQN. 60:

{dot over (W)} _(cmp) _(_) _(des) ={dot over (m)} _(cmp) _(_) _(des) ·C_(p)·(ΔT _(lp) _(_) _(cmp) +ΔT _(hp) _(_) _(cmp))  EQN. 60

The desired turbine power, {dot over (W)}_(trb) _(_) _(des), is setequal to the desired compressor power, {dot over (W)}_(cmp) _(_) _(des),as shown below in EQN. 61.

{dot over (W)} _(trb) _(_) _(des) ={dot over (W)} _(cmp) _(_)_(des),  EQN. 61

It should be noted that, although EQN. 61 appears to indicate nomechanical losses, mechanical losses were previously accounted for inthe turbine efficiency maps used in EQNS. 58 and 59.

The EGR cooler and valve model module 925 receives the desired EGR massflow for slow control, {dot over (m)}_(egr) _(_) _(slow) _(_) _(des), aswell as the desired intake manifold pressure, P_(im) _(_) _(des), an EGRcooler mass flow correction factor, CF_(egrc), and an EGR valve massflow correction factor, CF_(egrv), An exhaust manifold pressure minimum,P_(em) _(_) _(min), to achieve the desired EGR mass flow for slowcontrol, {dot over (m)}_(egr) _(_) _(slow) _(_) _(des)′ is determinedusing EQNS. 25 and 26. EQN. 26 is used to find the desired EGR cooleroutlet pressure, P_(egrco) _(_) _(des), that provides flow equal to thedesired EGR mass flow for slow control, {dot over (m)}_(egr) _(_)_(slow) _(_) _(des). This calculation is done with the EGR valveposition at its maximum, or slightly below the maximum to provide somereserve for control. In some embodiments, an iterative process can beused to find the solution. EQN. 25 is then used to find the exhaustmanifold pressure minimum, P_(em) _(_) _(min). In some embodiments, aniterative process can also be used to find this solution.

A desired exhaust manifold pressure, P_(em) _(_) _(des), is thencalculated by adding the exhaust manifold pressure minimum, P_(em) _(_)_(min), and desired exhaust manifold pressure offset, ΔP_(em) _(_)_(des), the result of which is limited to the exhaust manifold pressuremaximum, P_(em) _(_) _(max), as shown below in EQN. 62. The exhaustmanifold pressure maximum, P_(em) _(_) _(max), is a calculated parameterthat provides protection from high exhaust manifold pressure, as well ashigh engine delta pressure. High exhaust manifold pressure may causedamage to gaskets, seals, and the EGR cooler 665. Engine delta pressureis the difference between intake manifold pressure and exhaust manifoldpressure. If the exhaust manifold pressure exceeds the intake manifoldpressure by a large amount, the exhaust valves may be pushed open duringthe intake stroke of the engine 250. Such a condition may affectcombustion and could damage the engine and should be avoided.

P _(em) _(_) _(des)=minimum(P _(em) _(_) _(min) +ΔP _(em) _(_) _(des) ,P_(em) _(_) _(max))  EQN. 62

In some embodiments, it is desirable to filter the desired exhaustmanifold pressure, P_(em) _(_) _(des), to reduce actuator movement. Afirst order filter similar to that provided below in EQN. 75 can beused.

The desired exhaust manifold pressure, P_(em) _(_) _(des), is providedto the exhaust pressure control module 935. The exhaust pressure controlmodule 935 also receives the mass flow out of cylinders, {dot over(m)}_(cylso), the EGR mass flow, {dot over (m)}_(egr), and the exhaustmanifold pressure, P_(em).

A feed forward low pressure turbine mass flow, {dot over (m)}_(lp) _(_)_(trb) _(_) _(ff), is equal to the mass flow out of cylinders, {dot over(m)}_(cylso) minus the EGR mass flow, {dot over (m)}_(egr), as shownbelow in EQN. 63:

{dot over (m)} _(lp) _(_) _(trb) _(_) _(ff) ={dot over (m)} _(cylso)−{dot over (m)} _(egr)  EQN. 63

A closed loop low pressure turbine mass flow, {dot over (m)}_(lp) _(_)_(trb) _(_) _(cl), is equal to an exhaust manifold pressure proportionalgain, K_(p) _(_) _(em), multiplied by the difference between the desiredexhaust manifold pressure, P_(em) _(_) _(des) and the exhaust manifoldpressure, P_(em), as shown below in EQN. 64:

m _(lp) _(_) _(trb) _(_) _(cl) =K _(p) _(_) _(em)·(P _(em) −P _(em) _(_)_(des))  EQN. 64

A low pressure turbine mass flow setpoint, {dot over (m)}_(lp) _(_)_(trb) _(_) _(sp), is then equal to the sum of the feed forward lowpressure turbine mass flow, {dot over (m)}_(lp) _(_) _(trb) _(_) _(ff),and the closed loop low pressure turbine mass flow, {dot over (m)}_(lp)_(_) _(trb) _(_) _(cl), as shown below in EQN. 65:

{dot over (m)} _(lp) _(_) _(trb) _(_) _(sp) ={dot over (m)} _(lp) _(_)_(trb) _(_) _(ff) +{dot over (m)} _(lp) _(_) _(trb) _(_) _(cl)  EQN. 65

The term “setpoint” is used as opposed to the term “desired” in EQN. 65because a subsequent control step in the turbine and wastegate modelmodule 940 determines a desired mass flow that is achievable and asclose as possible to the setpoint of EQN. 65.

The turbine and wastegate model module 940 receives the low pressureturbine mass flow setpoint, {dot over (m)}_(lp) _(_) _(trb) _(_) _(sp),and the desired turbine power, {dot over (W)}_(trb) _(_) _(des), as wellas a variety of other parameters. The turbine and wastegate model module940 is used to determine a desired low pressure turbine mass flow, {dotover (m)}_(lp) _(_) _(trb) _(_) _(des), a desired turbine outletpressure, P_(trbo) _(_) _(des), a desired turbine outlet temperature,T_(trbo) _(_) _(des), and a desired wastegate position, u_(wg) _(_)_(des). Turbine mass flow and efficiency are determined using turbinemaps, temperature change across the turbine is calculated using thepressure ratio and efficiency, power is calculated using mass flow andtemperature change, and wastegate mass flow is determined using EQN. 29.A three-dimensional search is used to find the states that provide thedesired turbine power, {dot over (W)}_(trb) _(_) _(des), and achieve thelow pressure turbine mass flow setpoint, {dot over (m)}_(lp) _(_) _(trb)_(_) _(sp).

The first level of the search evaluates different desired turbine outletpressures, P_(trbo) _(_) _(des) with the goal of achieving the desiredturbine power, {dot over (W)}_(trb) _(_) _(des). The first level of thesearch is shown in and described with respect to a process 1000 in FIG.9. During each iteration of the process 1000, a second level search isperformed to evaluate different desired wastegate positions, u_(wg) _(_)_(des), with the goal of achieving the desired low pressure turbine massflow, {dot over (m)}_(lp) _(_) _(trb) _(_) _(des). The second level ofthe search is shown in and described with respect to a process 1100 inFIG. 10. During each iteration of the process 1100, a third level searchis performed to evaluate different turbine interstage pressures, P_(trb)_(_) _(inter), with the goal of achieving a low pressure turbine massflow, {dot over (m)}_(lp) _(_) _(trb), equal to the sum of a highpressure turbine mass flow, {dot over (m)}_(hp) _(_) _(trb), andwastegate mass flow, {dot over (m)}_(wg). During the third level search,the turbine maps are used to determine mass flow, efficiency,temperature, and power. The third level search applies to two-stageturbochargers. With a single turbocharge, these calculations would beperformed once for each turbine outlet pressure and wastegate valveposition combination. The third level of the search is shown in anddescribed with respect to a process 1200 in FIG. 11.

The process 1000 of FIG. 9 begins with receiving the desired turbinepower, {dot over (W)}_(trb) _(_) _(des), the exhaust manifold pressure,P_(em), and the DOC inlet pressure, P_(doci), at step 1005. In someembodiments, an after-treatment system inlet pressure is used. At step1010, a delta pressure across the turbine and the exhaust throttle,ΔP_(trb) _(_) _(et), is calculated as the difference between the exhaustmanifold pressure, P_(em), and the DOC inlet pressure, P_(doci), asshown below in EQN. 66:

ΔP _(trb) _(_) _(et) =P _(em) −P _(doci)  EQN. 66

Also at step 1010, a first factor, Factor1, and a factor adjustment,FactorAdj1, are respectively set to the values for the previous Factor1,PreviousFactor1, and an initial factor adjustment, FactorAdjInit, forvariable i=0. At step 1015, the variable, i, is compared to a maximumvalue for the variable, i_(max), which corresponds to a number ofiterations for the search. If the variable, i, is less than i_(max), theprocess 1000 proceeds to step 1020.

At step 1020, a desired turbine output pressure, P_(trbo) _(_) _(des),is calculated as the sum of the DOC inlet pressure, P_(doci), and theproduct of Factor1 and the delta pressure across the turbine and theexhaust throttle, ΔP_(trb) _(_) _(et), A as shown below in EQN. 67:

P _(trb) _(_) _(des) =P _(doci)+(Factor1·ΔP _(trb) _(_) _(et))  EQN. 67

At step 1020, FactorAdj1 is also reset to a value of FactorAdj1 dividedby 2. At step 1025, a desired wastegate position, u_(wg) _(_) _(des), alow pressure turbine mass flow, {dot over (m)}_(lp) _(_) _(trb), aturbine power, {dot over (W)}_(trb), and a turbine outlet temperature,T_(trbo), are calculated, as is described in more detail below withrespect to FIG. 10 and process 1100. At step 1030, the desired turbinepower, {dot over (W)}_(trb) _(_) _(des), is compared to the turbinepower, {dot over (w)}_(trb), calculated in step 1025. If the desiredturbine power, {dot over (W)}_(trb) _(—des) , is greater than theturbine power, {dot over (W)}_(trb), the process 1000 proceeds to step1035 where Factor1 is updated to a value of Factor1 plus FactorAdj1, andthe variable, i, is updated to a value of i+1 (step 1040). If thedesired turbine power, {dot over (W)}_(trb) _(_) _(des)′ is not greaterthan the turbine power, {dot over (W)}_(trb), the process 1000 proceedsto step 1045 where Factor1 is updated to a value of Factor1 minusFactorAdj1, and the variable, i, is updated to a value of i+1 (step1040). Steps 1015-1040 are repeated until the variable, i, is equal toi_(max). When the variable, i, is equal to i_(max) (i.e., no longer lessthan), the process proceeds to step 1050. At step 1050, the desiredturbine outlet temperature, T_(trbo) _(_) _(des), is set to thecalculated value of the turbine outlet temperature, T_(trbo), thedesired low pressure turbine mass flow, {dot over (m)}_(lp) _(_) _(trb)_(_) _(des), is set to the value for the calculated low pressure turbinemass flow, {dot over (m)}_(lp) _(_) _(trb), and PreviousFactor1 is setequal to Factor1. The process 1000 then outputs the desired turbineoutlet pressure, P_(trbo) _(_) _(des), the desired turbine outlettemperature, T_(trbo) _(_) _(des), the desired wastegate position,u_(wg) _(_) _(des), and the desired low pressure turbine mass flow, {dotover (m)}_(lp) _(_) _(trb) _(_) _(des). The process 1000 can then beexecuted again by the ECU 200.

The process 1100 of FIG. 10 begins with receiving the wastegate maximumposition, u_(wg) _(_) _(max), and the low pressure turbine mass flowsetpoint, {dot over (m)}_(lp) _(_) _(trb) _(_) _(sp), at step 1105. Atstep 1110, a second factor, Factor2, and a second factor adjustment,FactorAdj2, are respectively set to the values for the previous Factor2,PreviousFactor2, and an initial factor adjustment, FactorAdjInit, forvariable j=0. As step 1115, the variable, j, is compared to a maximumvalue for the variable, j_(max), which corresponds to a number ofiterations for the search. If the variable, j, is less than j_(max), theprocess 1100 proceeds to step 1120.

At step 1120, a desired wastegate position, u_(wg) _(_) _(des), iscalculated as the product of Factor2 and the wastegate maximum position,u_(wg) _(_) _(max), as shown below in EQN. 68:

u _(wg) _(_) _(des)=Factor2·u _(wg) _(_) _(max)  EQN. 68

At step 1120, FactorAdj2 is also reset to a value of FactorAdj2 dividedby 2. At step 1125, a low pressure turbine mass flow, {dot over(m)}_(lp) _(_) _(trb), a turbine power, {dot over (W)}_(trb), and aturbine outlet temperature, T_(trbo), are calculated, as is described inmore detail below with respect to FIG. 11 and process 1200. At step1130, the low pressure turbine mass flow setpoint, {dot over (m)}_(lp)_(_) _(trb) _(_) _(sp), is compared to the low pressure turbine massflow, {dot over (m)}_(lp) _(_) _(trb), calculated in step 1125. If thelow pressure turbine mass flow, {dot over (m)}_(lp) _(_) _(trb), isgreater than the low pressure turbine mass flow setpoint, {dot over(m)}_(lp) _(_) _(trb) _(_) _(sp), the process 1100 proceeds to step 1135where Factor2 is updated to a value of Factor2 plus FactorAdj2, and thevariable, j, is updated to a value of j+1 (step 1140). If the lowpressure turbine mass flow, {dot over (m)}_(lp) _(_) _(trb), is notgreater than the low pressure turbine mass flow setpoint, {dot over(m)}_(lp) _(_) _(trb) _(_) _(sp), the process 1100 proceeds to step 1145where Factor2 is updated to a value of Factor2 minus FactorAdj2, and thevariable, j, is updated to a value of j+1 (step 1140). Steps 1115-1140are repeated until the variable, j, is equal to j_(max). When thevariable, j, is equal to j_(max) (i.e., no longer less than), theprocess proceeds to step 1150. At step 1150, PreviousFactor2 is setequal to Factor2. The process 1100 then outputs the turbine outlettemperature, T_(trbo), the desired wastegate position, u_(wg) _(_)_(des), the low pressure turbine mass flow, {dot over (m)}_(lp) _(_)_(trb), and the turbine power, {dot over (W)}_(trb). The process 1100can then be executed again by the ECU 200.

The process 1200 of FIG. 11 begins with receiving a high pressureturbocharge speed, N_(hpt), a low pressure turbocharge speed, N_(lpt),the exhaust manifold pressure, P_(em), the exhaust manifold temperature,T_(em), the desired turbine outlet pressure, P_(trbo) _(_) _(des), andthe desired wastegate position, u_(wg) _(_) _(des), at step 1205. Atstep 1210, a delta turbine pressure, ΔP_(trb), is calculated as thedifference between the exhaust manifold pressure, P_(em), and thedesired turbine outlet pressure, P_(trbo) _(_) _(des), as shown below inEQN. 69:

ΔP _(trb) =P _(em) −P _(trbo) _(_) _(des)  EQN. 69

At step 1210, a third factor, Factor3, and a third factor adjustment,FactorAdj3, are respectively set to the values for the previous Factor3,PreviousFactor3, and an initial factor adjustment, FactorAdjInit, forvariable k=0. As step 1215, the variable, k, is compared to a maximumvalue for the variable, k_(max), which corresponds to a number ofiterations for the search. If the variable, k, is less than k_(max), theprocess 1200 proceeds to step 1220.

At step 1220, an interstage turbine pressure, P_(trb) _(_) _(inter) iscalculated as the sum of the desired turbine outlet pressure, P_(trbo)_(_) _(des), and the product of Factor3 and the delta turbine pressure,ΔP_(trb), as shown below in EQN. 70:

P _(trb) _(_) _(inter) =P _(trbo) _(_) _(des)+(Factor3·ΔP _(trb))  EQN.70

At step 1220, FactorAdj3 is also reset to a value of FactorAdj3 dividedby 2. At step 1225, a low pressure turbine mass flow, {dot over(m)}_(lp) _(_) _(trb), a high pressure turbine mass flow, {dot over(m)}_(hp) _(_) _(trb), a turbine outlet temperature, T_(trbo), aninterstage turbine temperature, T_(trb) _(_) _(inter), and a wastegatemass flow, {dot over (m)}_(wg), are calculated using theabove-referenced turbine maps. At step 1230, the low pressure turbinemass flow, m_(lp) _(_) _(trb), is compared to the sum of the highpressure turbine mass flow, {dot over (m)}_(hp) _(_) _(trb), and thewastegate mass flow, {dot over (m)}_(wg), calculated in step 1225. Ifthe sum of the high pressure turbine mass flow, {dot over (m)}_(hp) _(_)_(trb), and the wastegate mass flow, {dot over (m)}_(wg), is greaterthan the low pressure turbine mass flow, {dot over (m)}_(lp) _(_)_(trb), the process 1200 proceeds to step 1235 where Factor3 is updatedto a value of Factor3 plus FactorAdj3, and the variable, k, is updatedto a value of k+1 (step 1240). If sum of the high pressure turbine massflow, {dot over (m)}_(hp) _(_) _(trb), and the wastegate mass flow, {dotover (m)}_(wg), is not greater than the low pressure turbine mass flow,{dot over (m)}_(lp) _(_) _(trb), the process 1200 proceeds to step 1245where Factor3 is updated to a value of Factor3 minus FactorAdj3, and thevariable, k, is updated to a value of k+1 (step 1240). Steps 1215-1240are repeated until the variable, k, is equal to k_(max). When thevariable, k, is equal to k_(max) (i.e., no longer less than), theprocess 1200 proceeds to step 1250. At step 1250, the high pressureturbine power, {dot over (W)}_(hp) _(_) _(trb), and the low pressureturbine power, {dot over (W)}_(trb), are calculated, and PreviousFactor3is set equal to Factor3. Turbine power, {dot over (W)}_(trb), is alsocalculated as the sum of the low pressure turbine power, {dot over(W)}_(lp) _(_) _(trb), and the high pressure turbine power, {dot over(W)}_(hp) _(_) _(trb), as shown below in EQN. 71:

{dot over (W)} _(trb) ={dot over (W)} _(hp) _(_) _(trb) +{dot over (W)}_(lp) _(_) _(trb)  EQN. 71

The process 1200 then outputs the turbine outlet temperature, T_(trbo),the low pressure turbine mass flow, {dot over (m)}_(lp) _(_) _(trb), andthe turbine power, {dot over (W)}_(trb). The process 1200 can then beexecuted again by the ECU 200.

With reference once again to FIG. 8, the exhaust throttle model module945 receives the desired low pressure turbine mass flow, {dot over(m)}_(lp) _(_) _(trb) _(_) _(des), the desired turbine outlet pressure,P_(trbo) _(_) _(des), the desired turbine outlet temperature, T_(trbo)_(_) _(des), as well as a turbine mass flow correction factor, CF_(trb),and a DOC inlet pressure, P_(doci). The desired exhaust throttleposition, u_(et) _(_) _(des), is determined using the desired turbineoutlet pressure, P_(trbo) _(_) _(des), the desired turbine outlettemperature, T_(trbo) _(_) _(des), and the DOC inlet pressure, P_(doci),in EQN. 28. EQN. 28 can be rewritten to solve for the exhaust throttledischarge coefficient, C_(d) _(_) _(et), and a table with an input ofthe exhaust throttle discharge coefficient, C_(d) _(_) _(et), and outputof exhaust throttle position, u_(et), is used to find the desiredexhaust throttle position, u_(et) _(_) _(des). In some embodiments, aneffective area, which is equal to area times discharge coefficient, isused to determine desired exhaust throttle position, U_(et) _(_) _(des).This technique eliminates an area calibration parameter and uses a tablewith effective area as the input and position as the output.

The wastegate solenoid control module 950 of FIG. 8 is illustrated inmore detail in FIG. 12. The wastegate solenoid control module 950includes a wastegate delta pressure force module 1300, a wastegateposition to actuator force module 1305, an actuator model 1310, anactuator force to wastegate position module 1315, and a solenoid controlmodule 1320. The wastegate solenoid control module 950 receives thedesired wastegate position, U_(wg) _(_) _(des), from the turbine andwastegate model module 940, as well as an exhaust manifold pressure,P_(em), an intake manifold pressure, P_(im), and a barometric pressure,P_(baro). A wastegate force from delta pressure, F_(wg) _(_) _(dp), iscalculated in the wastegate delta pressure force module 1300 by takingthe difference between the exhaust manifold pressure, P_(em), andturbine interstage pressure, P_(trb) _(_) _(inter), and multiplying thedifference by wastegate area, A_(wg), as shown below in EQN. 72:

F _(wg) _(_) _(dp)=(P _(em) −P _(trb) _(_) _(inter))·A _(wg)  EQN. 72

A desired wastegate actuator force, F_(wg) _(_) _(act) _(_) _(des), iscalculated in the wastegate position to actuator force module 1305 by:(1) calculating a force from actuator spring compression, which is thedesired wastegate position, u_(wg) _(_) _(des), multiplied by wastegateactuator displacement maximum, d_(wg) _(_) _(act) _(_) _(max),multiplied by a wastegate actuator spring constant, k_(wg) _(_) _(act)_(_) _(spring); (2) subtracting the wastegate force from delta pressure,F_(wg) _(_) _(dp), adjusted for actuator linkage (i.e., multiply bypivot arm radius to wastegate valve, r_(wg) _(_) _(valve), and divide bypivot arm radius to wastegate actuator, r_(wg) _(_) _(act)); and (3)subtracting the wastegate spring preload, F_(wg) _(_) _(preload) asshown below in EQN. 73:

$\begin{matrix}{F_{{wg\_ act}{\_ des}} = {{u_{wg\_ des} \cdot d_{{wg\_ act}{\_ max}} \cdot k_{{wg\_ act}{\_ spring}}} - {\left( \frac{r_{wg\_ valve}}{r_{wg\_ act}} \right) \cdot F_{wg\_ dp}} - F_{wg\_ preload}}} & {{EQN}.\mspace{11mu} 73}\end{matrix}$

The wastegate spring preload, F_(wg) _(_) _(preload), will be a negativenumber, indicating compression with the sign convention shown in EQN.67. The spring preload, F_(wg) _(_) _(preload), tends to hold thewastegate valve 615 closed while the delta pressure across the wastegatevalve 615 tends to push it open. A desired wastegate actuator pressure,P_(wg) _(_) _(act) _(_) _(des), is calculated by dividing the desiredwastegate actuator force, F_(wg) _(_) _(act) _(_) _(des), by thewastegate actuator area, A_(wg) _(_) _(act), and adding barometricpressure, P_(baro), while limiting to intake manifold pressure, P_(im),as shown below in EQN. 74:

$\begin{matrix}{P_{{wg\_ act}{\_ des}} = {{minimum}\mspace{11mu} \left( {{P_{baro} + \frac{F_{{wg\_ act}{\_ des}}}{A_{wg\_ act}}},P_{im}} \right)}} & {{EQN}.\mspace{11mu} 74}\end{matrix}$

A wastegate actuator pressure, P_(wg) _(_) _(act), is modeled using afirst order filter with desired wastegate actuator pressure, P_(wg) _(_)_(act) _(_) _(des), as the input, as shown below in EQN. 75:

P _(wg) _(_) _(act) =P _(wg) _(_) _(act) _(_) _(des)+(P _(wg) _(_)_(act) _(_) _(previous) −P _(wg) _(_) _(act) _(_) _(des))·e ^(−T) ^(s)^(/τ) ^(wg)   EQN. 75

where T_(s) is the software task time step and τ_(wg) is the wastegateactuator pressure time constant. A wastegate actuator force, F_(wg) _(_)_(act), is then calculated by taking the difference between thewastegate actuator pressure, P_(wg) _(_) _(act), and the barometricpressure, P_(baro), and multiplying by wastegate actuator area, A_(wg)_(_) _(act), as shown below in EQN. 76:

F _(wg) _(_) _(act)=(P _(wg) _(_) _(act) −P _(baro))·A _(wg) _(_)_(act)  EQN. 76

A wastegate actuator force maximum, F_(wg) _(_) _(act) _(_) _(max), iscalculated in the actuator model module 1310 by taking the differencebetween intake manifold pressure, P_(im), and barometric pressure, andmultiplying by wastegate actuator area, A_(wg) _(_) _(act) as shownbelow in EQN. 77:

F _(wg) _(_) _(act) _(_) _(max)=(P _(im) −P _(baro))·A _(wg) _(_)_(act)  EQN. 77

A wastegate position estimate, u_(wg), is calculated in the actuatormodel module 1310 by rewriting EQN. 73 and using the wastegate actuatorforce, F_(wg) _(_) _(act), as shown below in EQN. 78:

$\begin{matrix}{u_{wg} = \frac{F_{wg\_ act} + {\left( \frac{r_{wg\_ valve}}{r_{wg\_ act}} \right) \cdot F_{wg\_ dp}} - F_{wg\_ preload}}{d_{{wg\_ act}{\_ max}} \cdot k_{{wg\_ act}{\_ spring}}}} & {{EQN}.\mspace{11mu} 78}\end{matrix}$

A wastegate position maximum, u_(wg) _(_) _(max), is calculated using asimilar equation but with the wastegate actuator force maximum, F_(wg)_(_) _(act) _(_) _(max), as shown below in EQN. 79:

$\begin{matrix}{u_{wg\_ max} = \frac{F_{{wg\_ act}{\_ max}} + {\left( \frac{r_{wg\_ valve}}{r_{wg\_ act}} \right) \cdot F_{wg\_ dp}} - F_{wg\_ preload}}{d_{{wg\_ act}{\_ max}} \cdot k_{{wg\_ act}{\_ spring}}}} & {{EQN}.\mspace{11mu} 79}\end{matrix}$

The relationship between wastegate solenoid current and actuationpressure is defined using a table. The output of the table is a feedforward wastegate solenoid current, i_(wg) _(_) _(sol) _(_) _(ff). Thex-input to the table is intake manifold pressure, P_(im), and they-input to the table is a normalized pressure that is calculated bytaking the difference between the desired wastegate actuator pressure,P_(wg) _(_) _(act) _(_) _(des), and barometric pressure, P_(baro), andthen dividing by the difference between intake manifold pressure,P_(im), and barometric pressure, P_(baro), as shown below in EQN. 80:

$\begin{matrix}{i_{{wg\_ sol}{\_ ff}} = {{WastegateSolenoidCurrentTable}\mspace{14mu} \left( {P_{im},\frac{P_{{wg\_ act}{\_ des}} - P_{baro}}{P_{im} - P_{baro}}} \right)}} & {{EQN}.\mspace{11mu} 80}\end{matrix}$

A wastegate solenoid proportional term, i_(wg) _(_) _(sol) _(_) _(prop),is calculated by multiplying the wastegate solenoid proportional gain,K_(p) _(_) _(wg), by the difference between the exhaust manifoldpressure, P_(em) (estimate), and an exhaust manifold pressure sensormeasurement, P_(em) _(_) _(sens), as shown below in EQN. 81:

i _(wg) _(_) _(sol) _(_) _(prop) =K _(p) _(_) _(wg)·(P _(em) −P _(em)_(_) _(sens))  EQN. 81

Numeric integration is used to update a wastegate solenoid integralterm, i_(wg) _(_) _(sol) _(_) _(int). At each time step in the software,the wastegate solenoid integral term, i_(wg) _(_) _(sol) _(_) _(int), isupdated by adding to the previous value, i_(wg) _(_) _(sol) _(_) _(int)_(_) _(previous), to the result of wastegate solenoid integral gain,K_(i) _(_) _(wg), multiplied by the difference between exhaust manifoldpressure, P_(em), and the exhaust manifold pressure sensor measurement,P_(em) _(_) _(sens), as shown below in EQN. 82:

i _(wg) _(_) _(sol) _(_) _(int) =i _(wg) _(_) _(sol) _(_) _(int) _(_)_(previous) +K _(i) _(_) _(wg)·(P _(em) −P _(em) _(_) _(sens))  EQN. 82

The desired wastegate solenoid current, i_(wg) _(_) _(sol) _(_) _(des),is equal to the sum of feed forward wastegate solenoid current, i_(wg)_(_) _(sol) _(_) _(ff), the wastegate solenoid current proportionalterm, i_(wg) _(_) _(sol) _(_) _(prop), and the wastegate solenoidcurrent integral term, i_(wg) _(_) _(sol) _(_) _(int), as shown below inEQN. 83:

i _(wg) _(_) _(sol) _(_) _(des) =i _(wg) _(_) _(sol) _(_) _(ff) +i _(wg)_(_) _(sol) _(_) _(prop) +i _(wg) _(_) _(sol) _(_) _(int)  EQN. 83

The wastegate solenoid current integral term, i_(wg) _(_) _(sol) _(_)_(int), the desired EGR valve position, u_(egr) _(_) _(des), and thedesired exhaust throttle valve position, U_(et) _(_) _(des), are thenprovided to the engine 250 to control the operation of the engine 250.

Thus, this disclosure provides, among other things, an air system stateobserver and control system including feed forward control forcontrolling the operation of an EGR valve, an exhaust throttle valve,and a wastegate valve for a diesel engine. Various features andadvantages are set forth in the following claims.

What is claimed is:
 1. A method of controlling exhaust gas temperaturefor an engine, the engine including an air system having an exhaustthrottle valve, the method comprising: receiving a parameter setpointcommand at an inverse engine model; monitoring parameters of the engineusing a plurality of sensors; receiving measured engine states based onthe monitored engine parameters from the plurality of sensors;generating measured engine state estimates and controlled engine stateestimates using an engine observer model, the controlled engine stateestimates being received by the inverse engine model; determining anobserver error based on a difference between the measured engine statesand the measured engine state estimates; generating model correctionsbased on the observer error, the model corrections being received by theinverse engine model; generating a desired exhaust throttle valveposition using the inverse engine model based on the parameter setpointcommand, the controlled engine state estimates, and the modelcorrections; and adjusting a position of the exhaust throttle valvebased on the desired exhaust throttle position.
 2. The method of claim1, further comprising determining a desired turbine outlet pressure. 3.The method of claim 2, wherein the desired turbine outlet pressure isdetermined based on a desired turbine power, an exhaust manifoldpressure, an after treatment system inlet pressure, and a turbine massflow setpoint.
 4. The method of claim 3, wherein the desired turbinepower is determined based on a desired compressor power.
 5. The methodof claim 4, wherein the desired compressor power is determined based ona desired intake manifold pressure and a desired compressor mass flow.6. The method of claim 1, wherein the parameter setpoint command isselected from the group consisting of: a desired diluent-to-air (“D/A”)ratio, a desired fuel-to-air (“F/A”) ratio, and a desired exhaustmanifold delta pressure.
 7. The method of claim 1, further comprisinggenerating a desired wastegate valve position using the inverse enginemodel based on the parameter setpoint command, the controlled enginestate estimates, and the model corrections; and adjusting a position ofthe wastegate valve based on the desired wastegate valve position. 8.The method of claim 7, wherein the desired wastegate valve position isdetermined based on a wastegate valve maximum position and a lowpressure turbine mass flow setpoint.
 9. The method of claim 8, whereinthe low pressure turbine mass flow setpoint is determined based on anexhaust manifold pressure and a desired exhaust manifold pressure. 10.The method of claim 9, wherein the desired exhaust manifold pressure isdetermined based on a minimum exhaust manifold pressure and a desiredexhaust manifold delta pressure.
 11. A system for controlling exhaustgas temperature, the system comprising: an engine including an airsystem and an exhaust throttle valve; a plurality of sensors formonitoring parameters of the engine; and an electronic control unitincluding a processor and a memory, the electronic control unit operableto receive a parameter setpoint command at an inverse engine model,monitor parameters of the engine using the plurality of sensors, receivemeasured engine states based on the monitored engine parameters from theplurality of sensors, generate measured engine state estimates andcontrolled engine state estimates using an engine observer model, thecontrolled engine state estimates being received by the inverse enginemodel, determine an observer error based on a difference between themeasured engine states and the measured engine state estimates, generatemodel corrections based on the observer error, the model correctionsbeing received by the inverse engine model, generate a desired exhaustthrottle valve position using the inverse engine model based on theparameter setpoint command, the controlled engine state estimates, andthe model corrections, and adjust a position of the exhaust throttlevalve based on the desired exhaust throttle position.
 12. The system ofclaim 11, wherein the electronic control unit is further operable todetermine a desired turbine outlet pressure.
 13. The system of claim 12,wherein the desired turbine outlet pressure is determined based on adesired turbine power, an exhaust manifold pressure, an after treatmentsystem inlet pressure, and a turbine mass flow setpoint.
 14. The systemof claim 13, wherein the desired turbine power is determined based on adesired compressor power.
 15. The system of claim 14, wherein thedesired compressor power is determined based on a desired intakemanifold pressure and a desired compressor mass flow.
 16. The system ofclaim 11, wherein the parameter setpoint command is selected from thegroup consisting of: a desired diluent-to-air (“D/A”) ratio, a desiredfuel-to-air (“F/A”) ratio, and a desired exhaust manifold deltapressure.
 17. The system of claim 11, wherein the electronic controlunit is further operable to generate a desired wastegate valve positionusing the inverse engine model based on the parameter setpoint command,the controlled engine state estimates, and the model corrections; andadjust a position of the wastegate valve based on the desired wastegatevalve position.
 18. The system of claim 17, wherein the desiredwastegate valve position is determined based on a wastegate valvemaximum position and a low pressure turbine mass flow setpoint.
 19. Thesystem of claim 18, wherein the low pressure turbine mass flow setpointis determined based on an exhaust manifold pressure and a desiredexhaust manifold pressure.
 20. The system of claim 19, wherein thedesired exhaust manifold pressure is determined based on a minimumexhaust manifold pressure and a desired exhaust manifold delta pressure.